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Cluster analysis techniques applications in automobile insurance
(Athens University of Economics and Business, 2003-05) Tsompanaki, Evgenia; Athens University of Economics and Business, Department of Statistics; Frangos, Nikolaos
Thesis - Athens University of Economics and Business. Postgraduate, Department of Statistics
Negative binomial regression with application in autorating
(Athens University of Economics and Business, 1998) Koutsoumbos, Fotios V.; Athens University of Economics and Business, Department of Statistics; Frangos, Nikolaos
Thesis - Athens University of Economics and Business. Postgraduate, Department of Statistics
Pricing options with Black - Scholes model and applications in Athens derivatives exchange
(Athens University of Economics and Business, 2011-10) Toumpakaris, Nikolaos; Frangos, Nikolaos
Thesis - Athens University of Economics and Business. Postgraduate, Department of Statistics
Probabilistic models in financial mathematics
(2006-07-31) Καλπινέλλη, Ευαγγελία; Kalpinelli, Evangelia; Athens University of Economics and Business, Department of Statistics; Zazanis, Michael; Panas, Epaminondas; Frangos, Nikolaos
Ο στόχος ενός στοχαστικού προτύπου είναι να συνδυαστεί η ικανότητα της θεωρίας Πιθανοτήτων να αντιμετωπίσει την αβεβαιότητα με την ικανότητα της παραγωγικής λογικής να προσδιορίσει τη δομή. Το αποτέλεσμα είναι ένας πλουσιότερος και πιο εκφραστικός φορμαλισμός με ένα ευρύ φάσμα τομέων εφαρμογής. Η δυσκολία με τα στοχαστικά πρότυπα είναι ότι τείνουν να πολλαπλασιάσουν την υπολογιστική πολυπλοκότητα των στοχαστικών και ντετερμινιστικών παραγόντων τους. Αυτή η διατριβή είναι μια συνοπτική ανάπτυξη της Μωρίας Πιθανοτήτων, που δίνει κύρια έμφαση στη μαθηματική αυστηρότητα και στις λεπτομερείς ιδιότητες ορισμένων προτύπων παρά στις γενικές έννοιες. Οι τρεις κρίσιμες έννοιες τη θεωρίας Πιθανοτήτων, εκείνη της τυχαίας μεταβλητής και αυτές της κατανομής πιθανότητας και της χαρακτηριστικής συνάρτησης μιας τυχαίας μεταβλητής, αναπτύσσονται συστηματικά σε χώρους πιθανότητας, στα πρώτα τρία κεφάλαια της παρούσας διατριβής. Εξίσου αναπτύσσονται και το Κεντρικό Οριακό Θεώρημα και η θεωρία σχετικά με τις Απείρως Διαιρετές Κατανομές. Στη συνέχεια, έχοντας ήδη εισάγει τις θεμελιώδεις αρχές της Θεωρίας Πιθανοτήτων, παρουσιάζουμε ορισμένα άλλα πεδία αυτής της θεωρίας, με σκοπό και να καλύψουμε τα σημαντικότερα πεδία αλλά και για να κρατήσουμε μια ισχυρή σύνδεση με τις εφαρμογές στα χρηματοοικονομικά. Για να είμαστε αρκετά συγκεκριμένοι, όλες αυτές οι μάλλον περίπλοκες μαθηματικές έννοιες τις οποίες παρουσιάζουμε, όπως τα Martingales, η Κίνηση Brown και το Στοχαστικό Ολοκλήρωμα, είναι εκείνες που οι οικονομικοί αναλυτές χρησιμοποιούν για να περιγράφουν τη συμπεριφορά των αγορών ή για να δημιουργήσουν νέες υπολογιστικές μεθόδους. Τελικά, αξίζει να αναφέρει ότι η Θεωρία Πιθανοτήτων μπορεί να εφαρμοστεί σε διάφορες άλλες επιστήμες, όπως η Βιοπληροφορική, η Επίσημη Επιστημολογία, η Θεωρία Παιγνίων, η Ψυχολογία κλπ., αλλά η παρουσίαση αυτών των τομέων εφαρμογής ξεφεύγει από τους σκοπούς αυτής της εργασίας.
A study of optimal bonus-malus systems in automobile insurance using different underlying approaches
Tzougas, George J.; Τζουγάς, Γεώργιος Ι.; Athens University of Economics and Business, Department of Statistics; Frangos, Nikolaos
The parallel growth of accidents and casualties to the increasing number of motor vehicles during the twentieth century and up to our days, has led the actuarial scientists around the world to develop Bonus-Malus Systems (BMS) that penalize insureds responsible for one or more accidents by premium surcharges or maluses and reward claim-free policyholders by awarding them discounts or bonuses. The Bonus-Malus Systems have played a fundamental role in the automobile insurance since it holds a significant part of the non-life business of many companies. Furthermore, due to the enormous and still growing competitiveness of the market, the Bonus-Malus Systems should be efficient, penalizing the bad drivers and simultaneously competitive. A basic interest of the actuarial literature is the construction of an optimal or ‘ideal’ BMS defined as a system obtained through Bayesian analysis. The main objective of the current thesis will be the study of optimal Bonus-Malus Systems using different underlying approaches. The majority of optimal BMS assign to each policyholder a premium based on his number of claims (claim frequency) disregarding his/hers aggregate claim amount (claim severity). In this way, a policyholder who underwent an accident with a small size of loss will be unfairly penalized in the same way with a policyholder who had an accident with a big size of loss. Motivated by this, in chapter 2 we will present an optimal BMS based on the a posteriori frequency and the a posteriori severity component under the assumption that the number of claims is distributed according to the Negative Binomial distribution and that the losses of the claims are distributed according to the Pareto distribution. Also, we will present a generalized optimal BMS that is based both on the a priori and a posteriori classification criteria by incorporating a priori information for each policyholder in the above design. In chapter 3, we will present a classical optimal BMS that takes into account the claim frequency and one that takes into account both the claim frequency and the claim severity. This time the claim frequency is distributed according to the Geometric distribution and the claim severity is distributed according to the Pareto distribution again. In chapter 4 we will present an optimal BMS that uses a three parameters distribution the Hofmann’s distribution for modeling claim frequency. Furthermore, a non-parametric method, that permits a simple formulation of the stationary and transition probabilities in a portfolio, is presented for the construction of an optimal BMS. In chapter 5, our analysis is based on the fact that for the construction of optimal BMS the distribution of the number of claims is frequently chosen within the “mixed-Poisson” family. We will show the general properties of “mixed Poisson” family distributions and we will give a unifying approach of several particular cases including the geometrical, the P-Erlang, the Negative Binomial and the Poisson inverse gaussian distributions. Also, in order to avoid the problem of adjustment that is the thickness of the tails of the underlying distributions we will present a new family of “mixed-Poisson”, built upon “fatty-tailed” underlying distributions, the “P-rational’’ distributions. In chapter 6, we will present an alternative approach to BMS the Stochastic Vortices Model developed under the assumption that we have an open portfolio, i.e., we consider that a policy can be transferred from one insurance company to another and that the new policies that constantly arrive into a portfolio can be placed not only in the “starting class” but into any of the bonus classes. The Stochastic Vortices Model applies to populations divided into sub-populations which correspond to the transient states of homogeneous Markov chains. Also, by using the limit state probabilities of the Model we can estimate the Long Run Distribution for a BMS and calculate optimal bonus-malus scales. Furthermore, since the Stochastic Vortices Model allows the subscription and the annulment of policies in the portfolio it is an alternative approach to the usual BMS model and the fact that the population is taken as open renders it quite representative of the reality. Finally, in chapter 7 for the first time in actuarial literature, we will propose a combination of a Poisson- Inverse Gaussian distribution for modeling claim frequency and of a Pareto distribution for modeling claim severity for the construction of an optimal BMS.
Utility indifference pricing : application on weather derivatives
(Athens University of Economics and Business, 2011-05) Papanikolaou, Zoi G.; Frangos, Nikolaos
Thesis - Athens University of Economics and Business. Postgraduate, Department of Statistics

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