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 ...
show more
Download full text in PDF format (680.89 kB)
(Available only to registered users)
|
All items in National Archive of Phd theses are protected by copyright.
|
Usage statistics
VIEWS
Concern the unique Ph.D. Thesis' views for the period 07/2018 - 07/2023.
Source: Google Analytics.
Source: Google Analytics.
ONLINE READER
Concern the online reader's opening for the period 07/2018 - 07/2023.
Source: Google Analytics.
Source: Google Analytics.
DOWNLOADS
Concern all downloads of this Ph.D. Thesis' digital file.
Source: National Archive of Ph.D. Theses.
Source: National Archive of Ph.D. Theses.
USERS
Concern all registered users of National Archive of Ph.D. Theses who have interacted with this Ph.D. Thesis. Mostly, it concerns downloads.
Source: National Archive of Ph.D. Theses.
Source: National Archive of Ph.D. Theses.