Forward - backward stochastic differential equations with random coefficients and applications to finance

Abstract

The first part of this thesis studies forward and backward versions of the random Burgers equation (RBE) with stochastic coefficients. 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.In the second part, we study a class of infinite horizon fully coupled FBSDEs, that is stimulated by various continuous time future expectations models with random coefficients. Under standard Lipschitz and m ...
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DOI
10.12681/eadd/38952
Handle URL
http://hdl.handle.net/10442/hedi/38952
ND
38952
Alternative title
Προδρομικές - οπισθοδρομικές στοχαστικές διαφορικές εξισώσεις με τυχαίους συντελεστές και εφαρμογές στα χρηματοοικονομικά
Author
Kartala, Xanthi-Isidora of Georgios
Date
2016
Degree Grantor
Athens University Economics and Business (AUEB)
Committee members
Γιαννακόπουλος Αθανάσιος
Φράγκος Νικόλαος
Ζαζάνης Μιχαήλ
Κραββαρίτης Δ.
Στρατής Ι.
Karatzas I.
Daskalopoulou P.
Discipline
Natural SciencesMathematics
Keywords
Stochastic Burgers equation; Random coefficients; Generalized Cole – Hopf transformation; Contingent claim pricing; Future expectations; Infinite horizon FBSDEs; Stochastic viscosity solutions; Stochastic maximum principle
Country
Greece
Language
English
Description
164 σ.
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