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Collections :	Ιδρυματικό Αποθετήριο ΟΠΑ / AUEB Institutional Repository Σχολή Επιστημών και Τεχνολογίας της Πληροφορίας / School of Informatics Τμήμα Στατιστικής / Department of Statistics Μεταπτυχιακές Εργασίες / Postgraduate dissertations

Title :	Forward - backward stochastic differential equations with random coeffcients and applications to finance

Alternative Title :	Προδρομικές- οπισθοδρομικές στοχαστικές διαφορικές εξισώσεις με τυχαίους συντελεστές και εφαρμογές στα χρηματοοικονομικά

Creator :	Kartala, Xanthi-Isidora

Contributor :	Yannacopoulos, Athanasios (Επιβλέπων καθηγητής) Athens University of Economics and Business, Department of Statistics (Degree granting institution)

Type :	Text

Extent :	164p.

Language :	en

Abstract :	The first part of this thesis studies forward and backward versions of the random Burgers equation (RBE) with stochastic coeffcients. First, the celebrated Cole-Hopf transformation reduces the forward RBE to a forward random heat equation (RHE) that can be treated pathwise. Next we provide a connection between the backward Burgers equation and a system of forward backward stochastic differential equations (FBSDEs). Exploiting this connection, we derive a generalization of the Cole-Hopf transformation which links the backward RBE with the backward RHE and investigate the range of its applicability. Stochastic Feynman- Kac representations for the solutions are provided. Explicit solutions are constructed and applications to stochastic control and mathematical finance are discussed.

Abstract :

The first part of this thesis studies forward and backward versions of the random Burgers equation (RBE) with stochastic coeffcients. First, the celebrated Cole-Hopf transformation reduces the forward RBE to a forward random heat equation (RHE) that can be treated pathwise. Next we provide a connection between the backward Burgers equation and a system of forward backward stochastic differential equations (FBSDEs). Exploiting this connection, we derive a generalization of the Cole-Hopf transformation which links the backward RBE with the backward RHE and investigate the range of its applicability. Stochastic Feynman- Kac representations for the solutions are provided. Explicit solutions are constructed and applications to stochastic control and mathematical finance are discussed.

Subject :	Stochastic Differential Equations (BSDEs) Random burgers equation (In-)Finite horizon random (FBSDE)

Date Issued :	13-07-2016

Licence :

File: Kartala_2016.pdf

Type: application/pdf

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