Διδακτορικές διατριβές

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Bayesian model determination and nonlinear threshold volatility models
Petralias, Athanassios; Πετραλιάς, Αθανάσιος; Athens University of Economics and Business, Department of Statistics; Dellaportas, Petros; Ntzoufras, Ioannis
The purpose of this Thesis is to document an original contribution in the areas of model determination and volatility modeling. Model determination is the procedure that evaluates the ability of competing hypothesized models to describe a phenomenon under study. Volatility modeling in the present context, involves developing models that can adequately describe the volatility process of a financial time series. In this Thesis we focus on the development of efficient algorithms for Bayesian model determination using Markov Chain Monte Carlo (MCMC), which are also used to develop a family of nonlinear flexible models for volatility. We propose a new method for Bayesian model determination that incorporates several desirable characteristics, resulting in better mixing for the MCMC chain and more precise estimates of the posterior density. The new method is compared with various existing methods in an extensive simulation study, as well as more complex model selections problems based on linear regression, with both simulated and real data comprising of 300 to 1000 variables. The method seems to produce rather promising results, overperforming several other existing algorithms in most of the analyzed cases. Furthermore the method is applied to gene selection using logistic regression, with a famous dataset including 3226 genes. The problem lies in identifying the genes related to the presence of a specific form of breast cancer. The new method again proves to be more efficient when compared to an existing Population MCMC sampler, while we extend the findings of previous medical studies on this issue. We present a new class of flexible threshold models for volatility. In these models the variables included, as well as the number and location of the threshold points are estimated, while the exogenous variables are allowed to be observed on lower frequencies than the dependent variable. To estimate these models we use the new method for Bayesian model determination, enriched with new move types, the use of which is validated through additional simulations. Furthermore, we propose a comparative model based on splines, where the number and location of the spline knots is related to a set of exogenous variables. The new models are applied to estimate and predict the variance of the Euro-dollar exchange rate, using as exogenous variables a set of U.S. macroeconomic announcements. The results indicate that the threshold models can provide significantly better estimates and projections than the spline model and typical conditional volatility models, while the most important macroeconomic announcements are identified. The threshold models are then generalised to the multivariate case. Under the proposed methodology, the estimation of the univariate variances is only required, as well as a rather small collection of regression coefficients. This simplifies greatly the inference, while the model is found to perform rather well in terms of predictability. A detailed review of both the available algorithms for Bayesian Model determination and nonlinear models for financial time series is also included in this Thesis. We illustrate how the existing methods for model determination are embedded into a common general scheme, while we discuss the properties and advantages each method has to offer. The main argument presented is that there is no globally best or preferable method, but their relative performance and applicability, depends on the dataset and problem of interest. With respect to the nonlinear models for financial time series and volatility we present in a unified manner, the main parametric and nonparametric classes of these models, while there is also a review of event studies analyzing the effect of news announcements on volatility.
Statistical methodology for estimating patterns of demographic phenomena
Peristera, Paraskevi M.; Περιστερά, Παρασκευή Μ.; Athens University of Economics and Business, Department of Statistics; Kostaki, Anastasia
The main objective of this work is to develop statistical methodology for estimating patterns of demographic phenomena. The main topics are briefly described below. Several techniques have been proposed in the literature for graduating mortality data. An innovative topic for graduating mortality data is the use of kernel regression estimators. In this work we provide an analytical evaluation of the alternative kernel estimators as tools for graduating mortality data. In order to evaluate the efficiency and accuracy of kernel techniques for graduation purposes, we apply these to several empirical data sets and compare the results with those of classical graduation techniques. The interesting finding is that the Gasser-Muller estimator proves more adequate compared to other kernel-type regression estimators. The study of sex mortality differences is a topic that has been widely studied. Particular emphasis is given to the causes that provoke these differences as well as the evolution of the sex mortality gap through time. The gap between the mortality patterns of the two sexes significantly varies through ages exhibiting a pattern that became typical since the middle of the 20th century. This pattern consists of two humps, the first around age 20 and the second around age 60. However the literature lacks a model that captures this pattern. Therefore in this work a parametric model is developed for estimating the age-specific pattern of sex mortality differences over the whole age range. This model is useful for many purposes. In fact, such a model, eliminating the random variations of empirical data can serve for simplifying comparisons of the mortality patterns between sexes. Moreover, capturing the pattern into a limited set of parameter values, it can simplify comparisons of the shape and the severity of the mortality deviations of the two sexes, through space and time.In order to evaluate the performance of such a parametric representation, we fit the model to a variety of empirical data sets. The results suggest that a widening of the sex mortality differential is reflected through time. In addition in recent years, the modes of the two humps tend to move to higher ages, except of some Baltic and East-European countries. It is of course interesting to further investigate the reasons for which this sex mortality widening occurs in recent years.Furthermore, a parametric model is developed in order to graduate the age-specific patterns of fertility and nuptiality. Considering fertility, it is known that the age-specific fertility pattern has a typical shape common in all human populations through years. In recent years, a distorted fertility pattern is observed for the UK, the USA and Ireland characterised by a second hump at earlier ages. As expected, the existing models are unable to estimate the new shape of the fertility pattern and therefore the use of more appropriate representations is required. The model proposed here is able to capture both the old and the new distorted fertility pattern. In this work, this model is utilised for estimating the age-specific fertility pattern the age-specific parity rates of several European populations. The results reveal that the patterns of early-age fertility, previously confined to a few mostly English-speaking countries, are now more widely distributed in Europe. Another finding is that for countries with enhanced early-age fertility the pattern of first births also exhibits a strongly intense hump in younger ages and even stronger than the pattern of total fertility. Furthermore the fertility pattern of the USA when differentiated by the ethnicity of the mother is quite heterogeneous. These facts provide a strong evidence of heterogeneity in the female populations associated not only to the marital status, race and birth order but also to the educational level, social and economic status as well as the religiosity of the mothers. The model proposed is also adequate for estimating the age-specific pattern of nuptiality. To evaluate its adequacy, comparisons with existing models are provided, for several populations through time. The results indicate that these models generally show deviations between the empirical and estimated rates at the tails of the first-marriage distribution for the majority of populations. This might be an indication of heterogeneity in these populations and therefore, as shown here, mixture modes are more adequate for fitting the nuptiality pattern of modern populations.
Fault-specific insurance pricing, reserving and CAT bond design for seismic risk assessment; the case of Greece
(2023-05-08) Λουλούδης, Εμμανουήλ; Louloudis, Emmanouil; Athens University of Economics and Business, Department of Statistics; Yannacopoulos, Athanasios; Tsekrekos, Andrianos; Psarakis, Stelios; Kyriakidis, Epaminondas; Pinto, Alberto-Adrego; Pinheiro, Diogo; Zimbidis, Alexandros
Κύριος σκοπός της διατριβής είναι η στοχαστική μοντελοποίηση και ποσοτικοποίηση του σεισμικού κινδύνου στο πλαίσιο της ασφάλισης του συγκεκριμένου κινδύνου. Θέτει τη βάση για τις πιο ορθές αναλογιστικές αποφάσεις των εμπλεκόμενων μερών, όπως η τιμολόγηση ασφαλίστρων, ο υπολογισμός του απαιτούμενου κεφαλαίου φερεγγυότητας και ο σχεδιασμός του αντίστοιχου ομολόγου καταστροφής. Τα σεισμικά μοντέλα που χρησιμοποιούνται ευρέως στην ασφαλιστική αγορά (κατά κύριο λόγο διαδικασίες Poisson) είναι βασισμένα σε ιστορικούς καταλόγους, οι οποίοι παρέχουν σχετική πληροφορία κάποιον εκατοντάδων ετών. Αντίθετα, ο μηχανισμός προσομοίωσης που παρουσιάζεται στη διατριβή βασίζεται στη γεωμετρία των ρηγμάτων, η οποία καλύπτει πληροφορία έως και 15 χιλιάδων ετών στο παρελθόν ώστε να εξαχθούν αξιόπιστα αναλογιστικά μεγέθη. Επιπρόσθετα, πολύγωνα Voronoi ή το επιδημικό μοντέλο ETAS χρησιμοποιούνται για την μοντελοποίηση των ιστορικών καταλόγων αντί τυπικών διαδικασιών Poisson και συνεχείς καμπύλες τρωτότητας αντί διακριτών και πιο αβέβαιων πινάκων πιθανοτήτων ζημίας. Καθώς παρόμοια μοντέλα της αγοράς είναι κατασκευασμένα ώστε να παράγουν τιμολόγηση ανά περιοχές, στην εργασία αυτή έχει επιτευχθεί ακρίβεια ανά συντεταγμένη χρήσιμη για μια ασφαλιστική εταιρεία για πλήρη γνώση του χαρτοφυλακίου κτιρίων της ώστε να μπορεί η ασφαλιστική εταιρεία να αποφύγει ή να διαχειριστεί καταστάσεις αντιεπιλογής. Επιπρόσθετα, οι μεγάλης κλίμακας καταστροφικές αποζημιώσεις του σεισμού καθιστούν τις αντασφαλιστικές εταιρείες ανίκανες να διαχειριστούν μόνες τους τα έξοδα αυτά. Για τον λόγο αυτό, η ασφαλιστική αγορά δημιούργησε τα ομόλογα καταστροφής ώστε να μεταφέρεται ο εν λόγω κίνδυνος στους επενδυτές της αγοράς κεφαλαίων. Στην παρούσα διατριβή, διεξάγεται ο σχεδιασμός και η τιμολόγηση του σχετικού ομολόγου καταστροφής συναρτήσει του προτεινόμενου σεισμικού μοντέλου χρησιμοποιώντας είτε αμιγώς στατιστικές προεξοφλητικές μεθόδους είτε σε συνδυασμό με μηχανικής μάθησης λαμβάνοντας υπόψη και τον πιστωτικό κίνδυνο κάθε εκδότη. Τα ομόλογα αυτά μπορούν να εκδοθούν για την αποτελεσματική αντιμετώπιση των οικονομικών συνεπειών ισχυρών σεισμών.
Towards a pan-European pension system: an initial approach
(2022-03-01) Kardiasmenos, Panagiotis S.; Καρδιασμένος, Παναγιώτης; Athens University of Economics and Business, Department of Statistics; Zazanis, Michael; Karlis, Dimitrios; Christopoulos, Apostolos; Katsampoxakis, Ioannis; Tzougas, George; Pantelous, Athanasios; Fragos, Nikolaos
Pension systems in the European Union are examined in this dissertation through an extensive statistical analysis of the aggregated figures by country. However, before this detailed, comparative and partial research of the data, a comparative-historical analysis is considered necessary. According to the objectives given, the first chapter will present a brief historical overview of the theory of pension systems. The second chapter will be dedicated to the nineteen European countries. For each state there will be:a presentation of the general information of the pension system,a brief historical review of its formation in conjunction with the current situation in accordance with the latest reforms of each countryand finally the challenges facing each country's pension system.In Chapter 3, a stratigraphic analysis of the total population of the Eurozone countries will be carried out. At the end of the section the ratio between employees and recipients of benefits will be calculated both in each Eurozone country and for the whole Eurozone as well.Chapter 4 lays the foundations and forms the proposal for a single Pan-European insurance system of the first pillar. This chapter examines different scenarios and versions in order to arrive at the proposed model. The findings in each case are also analyzed and the system with the most efficient characteristics is selected.Chapter 5 records the result of the possible application of the proposed Pan-European insurance system to the data of a Eurozone country. A comparison is made of the viability of the country's insurance system, as it exists with the proposed one, and the benefits and losses created by this application are recorded.The last chapter of the dissertation will discuss the possible effects of the implementation of the proposed model and will present thoughts for further research and improvement in the proposal.
A modelling approach for correlated binary outcomes
Αθανασοπούλου, Ιωάννα; Athanasopoulou, Ioanna; Athens University of Economics and Business, Department of Statistics; Δελλαπόρτας, Πέτρος; Καρλής, Δημήτριος; Τσιαμυρτζής, Παναγιώτης; Πεντελή, Ξανθή; Μουστάκη, Ειρήνη; Βιτωράτου, Σίλια; Βασδέκης, Βασίλειος
Σκοπός της παρούσης διατριβής είναι η συμβολή στην μοντελοποίηση της δομής συσχέτισης μεταξύ δυαδικών δεδομένων κοινής ομάδας. Το μοντέλο που αναπτύχθηκε βασίζεται σε μια αναπαράσταση της από κοινού πιθανότητας όπου η συσχέτιση των παρατηρήσεων κάθε ομάδας έχει ενσωματωθεί ως συνάρτηση μιας παραμέτρου και των περιθωριακών πιθανοτήτων των μελών της ομάδας, με το επιστημονικό ενδιαφέρον να επικεντρώνεται στην παράμετρο συσχετισμού καθώς και στους συντελεστές της παλινδρόμησης που αντιστοιχούν στις περιθωριακές πιθανότητες των δυαδικών παρατηρήσεων. Μια κατασκευαστική τεχνική που έχει προταθεί από τους Oman και Zucker χρησιμοποιείται ώστε να οριστούν δυαδικές μεταβλητές με δεδομένες περιθωριακές πιθανότητες και με απλές παραμετρικές δομές για τη συσχέτιση μεταξύ των ζευγών των παρατηρήσεων, οι οποίες προκύπτουν από τις κοινές πιθανότητες των μεταβλητών. Συγκεκριμένα, η παράμετρος που συνδέεται με τη συσχέτιση εκφράζει τη σχετική θέση της από κοινού πιθανότητας ζεύγους παρατηρήσεων μεταξύ της ανεξαρτησίας και της μέγιστης συσχέτισης. Επιπλέον, είναι μια μέθοδος κοινής πιθανοφάνειας που χρησιμοποιεί την αναπαράσταση του Bahadur, η οποία βασίζεται στην αποσύνθεση της από κοινού κατανομής στην κατανομή υπό ανεξαρτησία και σε ένα διορθωτικό παράγοντα που ενσωματώνει τη συσχέτιση εντός των ομάδων. Στο τρέχον πρότυπο θα χρησιμοποιηθεί η προσέγγιση 2ης τάξης, όπου υιοθετείται η υπόθεση των μηδενικών συσχετίσεων τάξης μεγαλύτερης του δύο. Για την εκτίμηση των παραμέτρων του μοντέλου χρησιμοποιούνται Μπεϋζιανές μέθοδοι εκτίμησης MCMC, λόγω δυσκολίας προσέγγισης μέσω αναλυτικών μεθόδων εκτίμησης.Εξετάζονται διάφορα σχήματα μοντελοποίησης της παραμέτρου συσχέτισης με τα πιο αποτελεσματικά από αυτά να είναι το απλό μοντέλο όπου όλες οι ομάδες έχουν κοινή παράμετρο συσχέτισης και το μοντέλο που η παράμετρος συσχέτισης μοντελοποιείται ως συνάρτηση ενός γραμμικού συνδυασμού ανεξάρτητων μεταβλητών. Περαιτέρω μοντέλα έχουν εξεταστεί όπου οι περιθωριακές πιθανότητες επηρεάζονται μέσω τυχαίων επιδράσεων παρατηρήσεως ή ομάδας, ή η παράμετρος συσχετισμού επηρεάζεται από τυχαία επίδραση της ομάδας, αλλά προέκυψαν ζητήματα σύγκλισης. Η απόδοση των μοντέλων εξετάστηκε σε προσομοιωμένα και πραγματικά σύνολα δεδομένων.
Bayesian evidence synthesis for the analysis of biomedical data
(2024-05-31) Αψεμίδης, Αναστάσιος; Apsemidis, Anastasios; Athens University of Economics and Business, Department of Statistics; Vasdekis, Vassilis; Kalogeropoulos, Kostas; Ntzoufras, Ioannis; Karlis, Dimitrios; Kyriakidis, Epaminondas; Kypraios, Theodore; Demiris, Nikolaos
Στην εποχή άνθησης της Στατιστικής και της Επιστήμης των Δεδομένων, η ανάλυση βιοϊατρικών δεδομένων κερδίζει συνεχώς την προσοχή ερευνητών και επαγγελματιών, οι οποίοι προσπαθούν να χρησιμοποιήσουν την πληθώρα πληροφορίας σε διαδικασίες λήψης αποφάσεων. Η Μπεϋζιανή μεθοδολογία, της οποίας η δημοτικότητα έχει επίσης αυξηθεί τις τελευταίες δεκαετίες λόγω της υπολογιστικής και στατιστικής προόδου σε μεθόδους προσομοίωσης Μόντε Κάρλο, παρέχει ένα συνεκτικό πλαίσιο σύνθεσης πληροφορίας από διαφορετικές πηγές. Έτσι, στοχεύουμε στη χρήση Μπεϋζιανών μοντέλων, για να εκτιμήσουμε σημαντικές ποσότητες στα πεδία τόσο των λοιμωδών όσο και των μη λοιμωδών ασθενειών. Όσον αφορά τις λοιμώδεις ασθένειες, ασχολούμαστε με την πανδημία Covid-19 και, συγκεκριμένα, κατασκευάζουμε στοχαστικά διαμερισματικά μοντέλα διακριτού χρόνου βασισμένα στο λανθάνον επίπεδο των καταγεγραμμένων και μη κρουσμάτων, ώστε να εκτιμήσουμε τo ρυθμό αναπαραγωγής και το ποσοστό των παρατηρούμενων κρουσμάτων. Επίσης, αντιμετωπίζουμε το πρόβλημα υπό το πρίσμα των δυναμικών συστημάτων με στόχο την ανάπτυξη διορατικότητας, αλλά και την κατασκευή ποσοτήτων κατάλληλων για υποστήριξη λήψης αποφάσεων. Στο πλαίσιο των μη λοιμωδών ασθενειών, προτείνουμε μεθόδους παρεκβολής της καμπύλης επιβίωσης, λαμβάνοντας υπόψη προβολές της θνησιμότητας, με στόχο να εκτιμήσουμε τα χρόνια ζωής που κερδίζονται, όταν εφαρμόζεται μία θεραπεία αντί κάποιας άλλης. Η μεθοδολογία παρουσιάζεται μέσα από τρία παραδείγματα που απασχολούν την ιατρική κοινότητα και αφορούν τον καρκίνο του μαστού, το μεταστατικό μελάνωμα και την καρδιακή αρρυθμία.
The generalized waring process - statistical inference and applications
(2021) Zografi, Mimoza S.; Ζωγράφη, Μιμόζα; Athens University of Economics and Business. Department of Statistics; Teugels, Jef; Dimaki, A.; Zazanis, Michael; Zografos, Constantinos; Balakrishnan, Narayanaswamy; Katti, S. K.; Xekalaki, Evdokia
Σ’ αυτήν την διατριβή αναπτύσσουμε μια θεωρία της Γενικευμένης Ανέλιξης Waring που σχετίζεται με μια μεγάλη ποικιλία εφαρμογών. Ειδικότερα, ορίζουμε πρώτα την Γενικευμένη Ανέλιξη Waring στην πραγματική ευθεία ως στατική, αλλά μη ομοιογενή ανέλιξη Markov. Παρέχεται μία εφαρμογή στο πλαίσιο μοντελοποίησης της πρόσβασης στο διαδίκτυο και εφαρμόζεται σε πραγματικά δεδομένα. Στην συνέχεια κατασκευάζουμε την Γενικευμένη Ανέλιξη Waring σε έναν πλήρη διαχωρίσιμο μετρικό χώρο. Η Γενικευμένη Ανέλιξη Waring ορίζεται στον Rd . Αποδεικνύοντας ένα αριθμό ιδιοτήτων της όπως προσθετικότητα, στασιμότητα, εργοδικότητα και διαταξιμότητα, επιδεικνύουμε ότι η νέα ανέλιξη είναι απολύτως ικανοποιητική για στατιστικές εφαρμογές.
Bayesian modelling of high dimensional financial data using latent gaussian models
Alexopoulos, Angelis N.; Αλεξόπουλος, Αγγελής Ν.; Athens University of Economics and Business, Department of Statistics; Dellaportas, Petros; Papaspiliopoulos, Omiros
The present thesis deals with the problem of developing statistical methodology for modellingand inference of high dimensional financial data. The motivation of our research wasthe identification of infrequent and extreme movements, which are called jumps, in the pricesof the 600 stocks of Euro STOXX index. This is known in the financial and statistical literatureas the problem of separating jumps from the volatility of the underlying process whichis assumed for the evolution of the stock prices.The main contribution of the thesis is the modelling and the development of methodsfor inference on the characteristics of the jumps across multiple stocks, as well as across thetime horizon. Following the Bayesian paradigm we use prior information in order to modela known characteristic of financial crises, which is that jumps in stock prices tend to occurclustered in time and to a↵ect several markets within a sort period of time. An improvementin the prediction of future stock prices has been achieved.The proposed model combines the stochastic volatility (SV) model with a multivariatejump process and belongs to the very broad class of latent Gaussian models. Bayesian inferencefor latent Gaussian models relies on a Markov chain Monte Carlo (MCMC) algorithmwhich alternates sampling from the distribution of the latent states of the model conditionalon the parameters and the observations, and sampling from the distribution of the parametersof the model conditional on the latent states and the observations. In the case of SVmodels with jumps, sampling the latent volatility process of the model is not a new problem.Over the last few years several methods have been proposed for separating the jumps fromthe volatility process but there is not a satisfactory solution yet, since sampling from a highdimensional nonlinear and non-Gaussian distribution is required. In the present thesis wepropose a Metropolis-Hastings algorithm in which we sample the whole path of the volatilityprocess of the model without using any approximation. We compare the resulting MCMCalgorithm with existing algorithms. We apply our proposed methodology on univariate SVwith jumps models in order to identify jumps in the stock prices of the real dataset thatmotivated our research.To model the propagation of the jumps across stocks and across time we combine the SVmodel with a doubly stochastic Poisson process, also known as Cox process. The intensityof the jumps in the Poisson process is modelled using a dynamic factor model. Furthermore,we develop an MCMC algorithm to conduct Bayesian inference for the parameters and thelatent states of the proposed model. We test the proposed methods on simulated data and weapplied them on our real dataset. We compare the prediction of future stock prices using theproposed model with the predictions obtained using existing models. The proposed modelprovides better predictions of future stock prices and this is an indication for a predictablepart of the jump process of SV models.IIIThe MCMC algorithm that is implemented in order to conduct Bayesian inference forthe aforementioned models is also employed on a demographic application. More precisely,within the context of latent Gaussian models we present a novel approach to model andpredict mortality rates of individuals.
Financial analysis of demographic ageing effect on pharmaceutical expenditure of Greece
(2014-07) Politi, Anastasia S.; Πολίτη, Αναστασία, Σ.; Athens University of Economics and Business, Department of Statistics; Φράγκος, Νικόλαος
The study aims to take a thorough look at the generating process of Greece’s pharmaceutical expenditure volatility taking into consideration latent cost synthesis differentiations among distinct morbidity areas. It uses frequency-severity models that decompose pharmaceutical demand of prescription drugs (Rxs) into a frequency component (claim frequency counts) and a severity component (claim size). It encompasses linear stochastic forms that treat health expenditure as an age-dependent branching process. The models also comprise the therapeutic category of Rxs as a controllable factor of population morbidity.Motivated by official population statistics which signal the impending serious growth of seniors’ portion within the following decades, globally and particularly in Greece, this dissertation presents estimating results of demographic senescence effects on pharmaceutical expenditure in the long run, through the implementation of projections for distinct therapeutic areas.Up to date literature review does not show any frequency – severity analysis conducted for pharmaceutical care data, neither at an international level, nor at the national level where the integrated information systems were developed with delay in relation to European systems. This study focused on this specific methodology and attempted to fill this knowledge gap in theVIdomain of healthcare by producing not only general estimates for the entire study population but also analytical results for sub-populations with distinct morbidity characteristics. As regards the principal aim of this study, namely, the estimation of the impact of aging on pharmaceutical expenditure, it is suggested that this study can bring substantial contribution to this cognitive field, as it includes the assessment of relevant results for sub-populations with distinct morbidity characteristics, which to the knowledge of the author, is a novel approach according to up to date literature data regarding Greece.According to the results, frequency effects play the key role towards severity ones in the generating process of pharmaceutical claim and loss intensity, this norm does not however apply within each therapeutic category. Pharmaceutical spending associated especially with the reimbursement of drugs for the genito-urinary system, the ophthalmological diseases, the antineoplastic and immunomodulating agents and the respiratory system, is more susceptible to the advent of the demographic aging risk.
Μοντελοποίηση των χρόνων προετοιμασίας παραγγελιών σε διαδικασία Detail Picking
(2007-11) Οικονόμου, Ιωάννης; Οικονομικό Πανεπιστήμιο Αθηνών, Τμήμα Στατιστικής; Ζαζάνης, Μιχαήλ
Διπλωματική εργασία - Οικονομικό Πανεπιστήμιο Αθηνών. ΜΠΣ, Τμήμα Στατιστικής με κατεύθυνση "Ποσοτικές Μέθοδοι στη Λήψη Αποφάσεων"
Discrete, continuous and machine learning models with applications in credit risk
(2023-09-13) Γεωργίου, Κυριάκος; Georgiou, Kyriakos; Athens University of Economics and Business, Department of Statistics; Xanthopoulos, Stylianos; Tsekrekos, Andrianos; Zazanis, Michael; Psarakis, Stelios; Siettos, Konstantinos; Weber, Gerhard-Wilhelm; Yannacopoulos, Athanasios
Η μοντελοποίηση πιστωτικού κινδύνου είναι ένας ταχέως αναπτυσσόμενος και δυναμικός κλάδος των μαθηματικών της χρηματοοικονομικής, με σημαντικές εφαρμογές, όπως έχει αποδειχθεί και ιστορικά. Συγκεκριμένα, η τελευταία οικονομική κρίση κατέστη σαφές ότι τα μοντέλα εκτίμησης πιστωτικού κινδύνου θα πρέπει να χαρακτηρίζονται από μαθηματική ακρίβεια και σαφήνεια. Για τον λόγο αυτόν, τα πρόσφατα Διεθνή Πρότυπα Χρηματοοικονομικής Αναφοράς (ΔΠΧΑ) 9 έχουν εισάγει το πλαίσιο της πρόβλεψης στην εκτίμηση του πιστωτικού κινδύνου, αυξάνοντας μ’ αυτόν τον τρόπο και την ανάγκη για αυστηρή μαθηματική μοντελοποίηση. Σκοπός της παρούσας διδακτορικής διατριβής είναι να αναπτύξει και να εξερευνήσει τα μαθηματικά εργαλεία και μοντέλα που προκύπτουν απ’ αυτήν την ανάγκη, με γνώμονα συγκεκριμένα ανοιχτά προβλήματα που δημιουργούνται με τα νέα πρότυπα, καθώς και να εισάγει ένα πλαίσιο μαθηματικής μοντελοποιήσης που μπορεί να εκμεταλλευτούν οι επαγγελματίες του κλάδου.Η έρευνα ξεκινά με διακριτά μοντέλα, και συγκεκριμένα αλυσίδες Markov, που είναι βαθιά καθιερωμένα εργαλεία στον χώρο του πιστωτικού κινδύνου, αναπτύσσοντας ένα αναγκαίο μαθηματικό πλαίσιο για την αναφορά των πιστωτικών αξιολογήσεων που εξασφαλίζει τη συμμόρφωση με το ΔΠΧΑ. Στην συνέχεια, χρησιμοποιούμε στοχαστικά μοντέλα σε συνεχή χρόνο για την εκτίμηση πιθανοτήτων αθέτησης, αλλά και μελλοντικών πιστωτικών ζημιών. Πιο ειδικά, εξετάζουμε μια οικογένεια μοντέλων που εισάγουν και κρυφές μεταβλητές οι οποίες επηρεάζουν την εξέλιξη ενός πιστωτικού προϊόντος (π.χ., μακροοικονομικές μεταβλητές), και χρησιμοποιούμε τεχνικές βασισμένες σε ολοκληρωτικές και μερικές ολοκληρο-διαφορικές εξισώσεις για να περιγράψουμε και να αποδείξουμε σημαντικές μαθηματικές ιδιότητες των συσχετιζομένων πιθανοτήτων αθέτησης. Για να συνεισφέρουμε στην εφαρμοσιμότητα των προαναφερθέντων μεθοδολογιών, αναπτύσσουμε και εξετάσουμε αριθμητικές μεθόδους για την εκτίμηση των πιθανοτήτων αθέτησης. Χρησιμοποιούμε τις γνωστές τεχνικές διακριτοποίησης στις μερικές ολοκληρο-διαφορικές εξισώσεις που προκύπτουν κάτω από ένα εύρος μοντέλων, δείχοντας την ποικιλία των προβλημάτων που μπορούν να επιλυθούν με αυτές τις τεχνικές. Τέλος, εμπνευσμένοι από σύγχρονη έρευνα στον τομέα της μηχανικής εκμάθησης, θεωρούμε τρόπους με τους οποίους αυτή, και συγκεκριμένα τα μοντέλα νευρωνικών δικτύων (deep neural networks – DNN), μπορούν να χρησιμοποιηθούν για την εκτίμηση των πιθανοτήτων αθέτησης, λύνοντας τις αντίστοιχες εξισώσεις. Ολοκληρώνοντας, εξετάζουμε θεωρητικές και πρακτικές πτυχές αυτών των μοντέλων που πρέπει να λαμβάνονται υπόψιν στην εφαρμογή των μοντέλων αυτών και τη σύγκρισή τους καθιερωμένες αριθμητικές μεθόδους.
Bayesian analysis and model selection for contingency tables using power priors
(2022-03-21) Μαντζούνη, Αικατερίνη; Mantzouni, Katerina; Athens University of Economics and Business, Department of Statistics; Karlis, Dimitrios; Kateri, Maria; Tarantola, Claudia; Demiris, Nikolaos; Papastamoulis, Panagiotis; Vasdekis, Vassilis; Ntzoufras, Ioannis
Κεντρικός πυλώνας της παρούσας διδακτορικής διατριβής είναι η ανάπτυξη προτεινόμενης μεθοδολογίας για τη Μπεϋζιανή ανάλυση κατηγορικών μεταβλητών σε πίνακες συνάφειας με σκοπό την επιλογή του καταλληλότερου μοντέλου. Η προτεινόμενη μεθοδολογία περιλαμβάνει τον καθορισμό κατάλληλων εκ-των-προτέρων κατανομών, καθώς επίσης και υπολογιστικές τεχνικές για την εκτίμηση Μπεϋζιανών περιθώριων πιθανοφανειών, οι οποίες είναι απαραίτητες για τον υπολογισμό των εκ-των-υστέρων κατανομών στην Μπεϋζιανή σύγκριση και επιλογή του καταλληλότερου μοντέλου. Πιο συγκεκριμένα, η επιλογή κατάλληλης εκ-των-προτέρων κατανομής στη Μπεϋζιανή σύγκριση μοντέλων και των σχετικών ελέγχων είναι πολλές φορές προβληματική λόγω του γνωστού προβλήματος ευαισθησίας των εκ των υστέρων πιθανοτήτων και του παραδόξου των Barlett-Lindley. Το γεγονός αυτό οδήγησε στην ανάπτυξη αντικειμενικών Μπεϋζιανών τεχνικών, οι οποίες προτείνουν τη χρήση μη πληροφοριακών εκ-των-προτέρων κατανομών, όταν δεν υπάρχει καμιά εκ-των-προτέρων πληροφορία για τα δεδομένα. Σε αυτο το πλαίσιο προτείνονται οι εκ-των-προτέρων κατανομές δύναμης. Για την εφαρμογή της προτεινόμενης μεθοδολογίας σε πίνακες συνάφειας, που στόχο έχει την επιλογή του καταλληλότερου μοντέλου συνάφειας, κατασκευάστηκαν δύο σενάρια εκ-των-προτέρων κατανομών με τη χρήση πλασματικών δεδομένων, τα οποία βασίστηκαν στις εκ-των-προτέρων κατανομές δύναμης. Εισάγουμε και εξετάζουμε δύο προτεινόμενους Μόντε Κάρλο εκτιμητές. Όλες οι τεχνικές εφαρμόστηκαν και ελέγχθηκαν σε πραγματικά δεδομένα αλλά και σε αναλυτικές μελέτες προσομοίωσης. Για να ελεγχθεί η εγκυρότητα της προτεινόμενης μεθοδολογίας χρησιμοποιήθηκαν κριτήρια αντικειμενικών μεθόδων Bayes, όπως συνέπεια επιλογής μοντέλων, συνέπεια πληροφορίας και το κριτήριο της αντιστοίχισης προβλεπτικών κατανομών. Τέλος, παρουσιάζεται η επέκταση της μεθοδολογίας στη χρήση μεθόδων Μπεϋζιανής ανάλυσης γραφικών μοντέλων σε πίνακες συνάφειας τριπλής εισόδου χρησιμοποιώντας εκ-των-προτέρων κατανομές δύναμης. Σε κάθε μοντέλο υπό συνθήκη ανεξαρτησίας αντιστοιχείται μια συγκεκριμένη παραγοντοποίηση των πιθανοτήτων των κελιών και εφαρμόζεται συζυγής ανάλυση, βασιζόμενη σε Dirichlet εκ-των-προτέρων κατανομές. Εκ-των-προτέρων κατανομές μοναδιαίας ερμηνευτικής πληροφορίας χρησιμοποιούνται σαν μέτρο σύγκρισης με στόχο να ελεγχθεί και να ερμηνευθεί η επίδραση οποιονδήποτε εκ-των-προτέρων κατανομών στον παράγοντα Bayes και κατ’ επέκταση στην διαδικασία επιλογής γραφικών μοντέλων.
Bayesian modeling and estimation for complex multiparameter problems with real applications
(2021) Koki, Constandina; Κοκή, Κωνσταντίνα; Athens University of Economics and Business, Department of Statistics; Meligkotsidou, Loukia; Karlis, Dimitrios; Dellaportas, Petros; Kypraios, Theodore; Fouskakis, Dimitris; Kalogeropoulos, Kostas; Vrontos, Ioannis
In the big data era, the study of complex multiparameter problems is more than necessary. The development of Machine Learning techniques enhanced the inferentialability of statistical models. In this direction, by leveraging Machine Learning techniques, we propose a new predictive Hidden Markov model with exogenous variables, within a Bayesian framework, for joint inference and variable selection. Wepropose a computational Markov Chain Monte Carlo algorithm that offers improved forecasting and variable selection performance, compared to existing benchmarkmodels. Our methodology is applied in various simulated and real datasets, such as realized volatility data and cryptocurrency return series. Furthermore, we exploit the Bayesian methodology in implementing the X-ray luminosity function of the ActiveGalactic Nuclei under the assumption of Poisson errors in the determination of X-ray fluxes and estimation uncertainties.
Actuarial modelling of claim counts and losses in motor third party liability insurance
(2013-07) Tzougas, George J.; Τζουγάς, Γεώργιος Ι.; Athens University of Economics and Business, Department of Statistics; Frangos, Nikolaos
Actuarial science is the discipline that deals with uncertain events where clearly theconcepts of probability and statistics provide for an indispensable instrument in themeasurement and management of risks in insurance and finance. An important aspectof the business of insurance is the determination of the price, typically calledpremium, to pay in exchange for the transfer of risks. It is the duty of the actuary toevaluate a fair price given the nature of the risk. Actuarial literature research covers awide range of actuarial subjects among which is risk classification and experiencerating in motor third-party liability insurance, which are the driving forces of theresearch presented in this thesis. This is an area of applied statistics that has beenborrowing tools from various kits of theoretical statistics, notably empirical Bayes,regression, and generalized linear models, GLM, (Nelder and Wedderburn, 1972).However, the complexity of the typical application, featuring unobservable riskheterogeneity, imbalanced design, and nonparametric distributions, inspiredindependent fundamental research under the label `credibility theory', now acornerstone in contemporary insurance mathematics. Our purpose in this thesis is tomake a contribution to the connection between risk classification and experiencerating with generalized additive models for location scale and shape, GAMLSS,(Rigby and Stasinopoulos, 2005) and finite mixture models (Mclachlan and Peel,2000). In Chapter 1, we present a literature review of statistical techniques that can bepractically implemented for pricing risks through ratemaking based on a priori riskclassification and experience rated or Bonus-Malus Systems. The idea behind a prioririsk classification is to divide an insurance portfolio into different classes that consistof risks with a similar profile and to design a fair tariff for each of them. Recentactuarial literature research assumes that the risks can be rated a priori usinggeneralized linear models GLM, (see, for example, Denuit et al., 2007 & Boucher etal., 2007, 2008). Typical response variables involved in this process are the number ofclaims (or the claim frequency) and its corresponding severity (i.e. the amount theinsurer paid out, given that a claim occurred). In Chapter 2, we extend this setupfollowing the GAMLSS approach of Rigby and Stasinopoulos (2005). The GAMLSSmodels extend GLM framework allowing joint modeling of location and shapeparameters. Therefore both mean and variance may be assessed by choosing a marginal distribution and building a predictive model using ratemaking factors asindependent variables. In the setup we consider, risk heterogeneity is modeled as thedistribution of frequency and cost of claims changes between clusters by a function ofthe level of ratemaking factors underlying the analyzed clusters. GAMLSS modelingis performed on all frequency and severity models. Specifically, we model the claimfrequency using the Poisson, Negative Binomial Type II, Delaporte, Sichel and Zero-Inflated Poisson GAMLSS and the claim severity using the Gamma, Weibull, WeibullType III, Generalized Gamma and Generalized Pareto GAMLSS as these models havenot been studied in risk classification literature. The difference between these modelsis analyzed through the mean and the variance of the annual number of claims and thecosts of claims of the insureds, who belong to different risk classes. The resulting apriori premiums rates are calculated via the expected value and standard deviationprinciples with independence between the claim frequency and severity componentsassumed. However, in risk classification many important factors cannot be taken intoaccount a priori. Thus, despite the a priori rating system, tariff cells will not becompletely homogeneous and may generate a ratemaking structure that is unfair to thepolicyholders. In order to reduce the gap between the individual's premium and riskand to increase incentives for road safety, the individual's past record must taken intoconsideration under an a posteriori model. Bonus-Malus Systems (BMSs) are aposteriori rating systems that penalize insureds responsible for one or more accidentsby premium surcharges or maluses and reward claim-free policyholders by awardingthem discounts or bonuses. A basic interest of the actuarial literature is theconstruction of an optimal or `ideal' BMS defined as a system obtained throughBayesian analysis. A BMS is called optimal if it is financially balanced for theinsurer: the total amount of bonuses must be equal to the total amount of maluses andif it is fair for the policyholder: the premium paid by each policyholder is proportionalto the risk that they impose on the pool. The study of such systems based on differentstatistical models will be the main objective of this thesis. In Chapter 3, we extend thecurrent BMS literature using the Sichel distribution to model the claim frequencydistribution. This system is proposed as an alternative to the optimal BMS obtained bythe Negative Binomial model (see, Lemaire, 1995). We also consider the optimalBMS provided by the Poisson-Inverse Gaussian distribution, which is a special caseof the Sichel distribution. Furthermore, we introduce a generalized BMS that takesinto account both the a priori and a posteriori characteristics of each policyholder, extending the framework developed by Dionne and Vanasse (1989, 1992). This isachieved by employing GAMLSS modeling on all the frequency models consideredin this chapter, i.e. the Negative Binomial, Sichel and Poisson-Inverse Gaussianmodels. In the above setup optimality is achieved by minimizing the insurer's risk.The majority of optimal BMSs in force assign to each policyholder a premium basedon their number of claims disregarding their aggregate amount. In this way, apolicyholder who underwent an accident with a small size of loss will be unfairlypenalized in comparison to a policyholder who had an accident with a big size of loss.Motivated by this, the first objective of Chapter 4 is the integration of claim severityinto the optimal BMSs based on the a posteriori criteria of Chapter 3. For this purposewe consider that the losses are distributed according to a Pareto distribution,following the setup used by Frangos and Vrontos (2001). The second objective ofChapter 4 is the development of a generalized BMS with a frequency and a severitycomponent when both the a priori and the a posteriori rating variables are used. Forthe frequency component we assume that the number of claims is distributedaccording to the Negative Binomial Type I, Poisson Inverse Gaussian and SichelGAMLSS. For the severity component we consider that the losses are distributedaccording to a Pareto GAMLSS. This system is derived as a function of the years thatthe policyholder is in the portfolio, their number of accidents, the size of loss of eachof these accidents and of the statistically significant a priori rating variables for thenumber of accidents and for the size of loss that each of these claims incurred.Furthermore, we present a generalized form of the one obtained in Frangos andVrontos (2001). Finally, in Chapter 5 we give emphasis on both the analysis of theclaim frequency and severity components of an optimal BMS using finite mixtures ofdistributions and regression models (see Mclachlan and Peel, 2000 & Rigby andStasinopoulos, 2009) as these methods, with the exception of Lemaire(1995), have notbeen studied in the BMS literature. Specifically, for the frequency component weemploy a finite Poisson, Delaporte and Negative Binomial mixture, while for theseverity component we employ a finite Exponential, Gamma, Weibull andGeneralized Beta Type II (GB2) mixture, updating the posterior probability. We alsoconsider the case of a finite Negative Binomial mixture and a finite Pareto mixtureupdating the posterior mean. The generalized BMSs we propose adequately integraterisk classification and experience rating by taking into account both the a priori and aposteriori characteristics of each policyholder.
Modeling multivariate time series
(2023-11-21) Tsamtsakiri, Panagiota; Τσαμτσακίρη, Παναγιώτα; Athens University of Economics and Business, Department of Statistics; Ntzoufras, Ioannis; Vrontos, Ioannis; Pedeli, Xanthi; Fokianos, Konstantinos; Ombao, Hernando; Barretto-Souza, Wanger; Karlis, Dimitrios
This thesis deals with the construction of multivariate Integer Generalized Au toregressive Conditional Heteroskedastic(INGARCH) and Conditional Autoregres sive Range(CARR) time series processes. The INGARCH(1,1) model has been alsostudied in multivariate case and implementations in 2 dimensions have been also pre sented recent years. The drawback was found at the restricted values of correlationcoefficient boundaries depending on the way of model’s construction. Based on afamily of copulas a multivariate INGARCH(1,1) model and a CARR(1,1) model arestudied considering interdependencies and self-dependencies respectively. Accordingto model’s complexity, its appropriateness and capability to study data with smallsample sizes are examined and provided with simulations. H-steps ahead forecast ing is considered by taking conditional expectation on volatilities and calculatingmarginal probability mass function.Firstly, considering univariate INGARCH models where volatilities are linearly orlog-linearly expressed offering more flexibility on conditions of stationarity respec tively, a Bayesian Trans-dimensional Markov Chain Monte Carlo is provided. At asecond stage a new alternative family of Sarmanov distribution is also presented inorder to ameliorate boundaries of correlation coefficient and comparison with theknown Sarmanov families are graphically discussed. A multivariate INGARCH(1,1)process is studied based on this alternative Sarmanov distribution and an imple mentation with daily crash counts on three towns in Netherlands is presented. Amultivariate Conditional Aytoregressive Range(CARR(1,1)) model assuming an ex ponential distribution and reconstructing correlation coefficients boundaries is dis cussed. The proposed model is illustrated on bivariate series from the fields ofrenewable sources.
Self-starting methods in Bayesian statistical process control and monitoring
(2021-10-26) Bourazas, Konstantinos; Μπουραζάς, Κωνσταντίνος; Ntzoufras, Ioannis; Demiris, Nikolaos; Psarakis, Stelios; Capizzi, Giovanna; Colosimo, Bianca Maria; Chakraborti, Subhabrata; Tsiamyrtzis, Panagiotis
In this dissertation, the center of attention is in the research area of Bayesian Statistical Process Control and Monitoring (SPC/M) with emphasis in developing self-starting methods for short horizon data. The aim is in detecting a process disorder as soon as it occurs, controlling the false alarm rate, and providing reliable posterior inference for the unknown parameters. Initially, we will present two general classes of methods for detecting parameter shifts for data that belong to the regular exponential family. The first, named Predictive Control Chart (PCC), focuses on transient shifts (outliers) and the second, named Predictive Ratio CUSUM (PRC), in persistent shifts. In addition, we present an online change point scheme available for both univariate or multivariate data, named Self-starting Shiryaev (3S). It is a generalization of the well-known Shiryaev’s procedure, which will utilize the cumulative posterior probability that a change point has been occurred. An extensive simulation study along with a sensitivity analysis evaluate the performance of the proposed methods and compare them against standard alternatives. Technical details, algorithms and general guidelines for all methods are provided to assist in their implementation, while applications to real data illustrate them in practice.
Modelling multivariate time series for count data
(2011-06) Pedeli, Xanthi; Athens University of Economics and Business, Department of Statistics; Karlis, D.
The study of time series models for count data has become a topic of special interest during the last years. However, while research on univariate time series for counts now flourishes, the literature on multivariate time series models for count data is notably more limited. The main reason for this is that the analysis of multivariate counting processes presents many more difficulties. Specifically, the need to account for both serial and cross–correlation complicates model specification, estimation and inference. This thesis deals with the class of INteger–valued AutoRegressive (INAR) processes, a recently popular class of models for time series of counts. The simple, univariate INAR(1) process is initially extended to the 2–dimensional space. In this way, a bivariate (BINAR(1)) process is introduced. Subsequently, the time invariant BINAR(1) model is generalized to a BINAR(1) regression model. Emphasis is given on models with bivariate Poisson and bivariate negative binomial innovations. The properties of the BINAR(1) model are studied in detail and the methods of moments, Yule-Walker and conditional maximum likelihood are proposed for the estimation of its unknown parameters. The small sample properties of the alternative estimators are examined and compared through a simulation experiment. Issues of diagnostics and forecasting are considered and predictions are produced by means of the conditional forecast distribution. Estimation uncertainty is accommodated by taking advantage of the asymptotic normality of maximum likelihood estimators and constructing appropriate confidence intervals for the h–step–ahead conditional probability mass function. A generalized specification of the BINAR(1) process, where cross–correlation between the two series receives contribution from two different sources, is also discussed. In this case, we mainly focus on a specific parametric case that arises under the assumption that the innovations follow jointly a bivariate Poisson distribution. The resulting joint distribution of the bivariate series is identified as an 8–parameters bivariate Hermite. At a second stage, the BINAR(1) process is extended to the multi–dimensional space. Thus, we define a multivariate integer–valued autoregressive process of order 1 (MINAR(1)) and examine its basic statistical properties. Such an extension is not simple and we emphasize on problems that occur, relating to selecting a reasonable innovation distribution as well as on problems related to inference. Apart from the general specification of the MINAR(1) process, we also study two specific parametric cases that arise under the assumptions of a multivariate Poisson and a multivariate negative binomial distribution for the innovations of the process. To overcome the computational difficulties of the maximum likelihood approach we suggest the method of composite likelihood. The performance of the two methods of estimation (i.e. maximum likelihood and composite likelihood) is compared through a small simulation experiment. Extensions to incorporate covariance information are also discussed. The proposed models are illustrated on multivariate count series from the fields of accident analysis, syndromic surveillance and finance.
Stochastic optimal control and stochastic differential games: applications in insurance
Baltas, Ioannis; Μπαλτάς, Ιωάννης; Athens University of Economics and Business, Department of Statistics; Yannacopoulos, Athanasios
The present thesis is divided into two parts, The first part begins with the development of a new approach to study the problem of optimal investment under asymmetric information. This approach heavily relies on stochastic optimal control techniques and in particular on the use of the Hamilton-Jacobi-Bellman equation. Then, we turn our attention to the introduction of inside information aspects to the insurance/reinsurance market. This accomplished by considering two firms: an insurer and a reinsurer and letting one of the firms, the insurer, posses some additional information which is hidden from the reinsurer. By employing the aforementioned approach, we are able to treat the problem of maximizing the expected utility from terminal wealth, for both firms, by taking explicitly into account their different information on the optimal decisions of the insurer. The aim of the second part is to study a robust-entropic optimal control problem between an insurance firm and Nature. However, a major obstacle arises, as the value of this problem is associated with a fully nonlinear partial differential equation that may not admit smooth solutions. In order to overcome this difficulty, we write this general problem as a normal form zero sum stochastic differential game with two players and resort to the classical theory developed by Fleming and Souganidis[42] in order to prove that the associated Bellman-Isaacs partial differential equation admits a unique continuous viscosity solution, which is the Nash value of the game. Furthermore, we state and prove a general verification theorem that allows to characterize the optimal controls of the players. Finally, we provide the connection of the robust-entropic control problem with the theory of convex risk measures and we conclude with the study of the asymptotic behavior of the aforementioned Bellman-Isaacs equation.
Adaptive designs in phase II clinical trials
(2013-09-23) Poulopoulou, Stavroula; Πουλοπούλου, Σταυρούλα; Athens University of Economics and Business. Department of Statistics; Karlis, Dimitrios; Dafni, Urania
Clinical trials play a very important role in the development process of new therapies. Recently there has been a rapid increase in theresearch and creation of new modern molecular agents, which makes necessary the development of more flexible and adaptive designs forthe implementation of clinical trials. The objective of adaptive designs is to ensure direct and dynamic control of the effectiveness and thesafety of a new treatment by allowing the adjustment of the elements of the study (i.e sample size), during the study, in such a way that wewill not sacrifice elements which are associated with the credibility of the study (i.e statistical power) and also issues which concern ethicalcharacteristics of the clinical trials.
Stochastic linear quadratic control problems with applications to insurance
Pantelous, Athanasios Α.; Παντελούς, Αθανάσιος Α.; Athens University of Economics and Business, Department of Statistics; Φράγκος, Νικόλαος
Τhis thesis aims to extend further the modelling and decision-making (control) methods techniques for the deeper investigation of several important actuarial (practical) problems. The major drive in this task is the application of stochastic linear-quadratic control methodologies into several actuarial processes. In more details, a significant contribution of this PhD thesis is the further understanding of the role of (stochastic) control theory in the specification of conceptual actuarial models and subsequently the transition towards the development of more formal dynamic models. A quite general discrete and continuous-time (stochastic) control framework, suitable for discussing a number of important issues arising in the analysis and the design of actuarial processes, is introduced. It will be described as a mean of integrating diverse areas where mainly linear system concepts are used. A general approach towards the definition of linear stochastic systems will also be given. Analytically, a) A discrete-time stochastic control multi-dimensional model for a quasi PAYGO social security system is introduced to allow the potential accumulation of a special (contingency) fund, which can oscillate deliberately absorbing fluctuations in the different system parameters involved. b) A more realistic approach for the management of a defined contribution pension scheme is proposed in the distribution phase (post-retirement period) providing a whole life assurance benefit. In that direction, it is assumed a stochastic framework for both mortality and investment risk and additionally suggested a correlation effect between the two separate risks .c) A stochastic control model is introduced for a pension fund which provides a variable death benefit to its members during the post-retirement period. The main framework model is described by two correlated fractional Brownian motions which correspond to investment and mortality risks, accordingly .d) The classical problem of premium rating within a heterogeneous portfolio of risks is investigated by using a continuous stochastic framework. The portfolio is divided into several classes where each class interacts with other. The risks are modelled dynamically by the means of a standard Brownian motion. This dynamic approach is also transferred to the design of the premium process. e) Finally, in the last work, the various claim reserving methods are discussed for non-life insurance systems. Furthermore, a dynamic control model with the associated stochastic differential equations is analytically designed describing the mechanisms of the payments and the reserving process, as well.

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