Backward stochastic differential equations with jumps are stable
type: CreativeWork
description: A backward stochastic differential equation is a stochastic differential equation whose terminal value is known, in contrast to a (forward) stochastic differential equation whose initial value is known, and whose solution has to be adapted to a given filtration. The main aim of this thesis is to provide the suitable framework for the stability of stochastic differential equations with jumps, hereinafter BSDEs or BSDE when we refer to a single object. With the term stability we understand the continuity of the operator that maps the standard data of a BSDE, a set which among others includes the terminal value of the BSDE and the filtration with respect to which the solution has to be adapted, to its solution. In other words, the stability property allows to obtain an approximation of the solution of the BSDE under interest, once we determine an approximation of the standard data of the BSDE under interest. In this thesis we provide a general wellposedness result of multidimensional BSDEs with stochastic Lipschitz generator and which is driven by a possibly stochastically discontinuous square-integrable martingale. The time horizon can be infinite and as already implicitly has been stated, the right-continuous filtration is allowed to be stochastically discontinuous. Moreover, we provide a framework under which the stability property of BSDEs is verified. This framework allows for both continuous-time and discrete-time L2 −type approximations, which can turn out to be particularly useful for the well-posedness of numerical schemes for BSDEs. These results are presented in the second and the fourth chapter of this thesis. In the third chapter the stability of martingale representations is obtained, a result which lies at the core of the stability property of BSDEs. The property of the stability of martingale representations is not only a useful tool for our current needs, but it is also an interesting result on its own. Roughly speaking, it amounts to the convergence o…
abstract: A backward stochastic differential equation is a stochastic differential equation whose terminal value is known, in contrast to a (forward) stochastic differential equation whose initial value is known, and whose solution has to be adapted to a given filtration. The main aim of this thesis is to provide the suitable framework for the stability of stochastic differential equations with jumps, hereinafter BSDEs or BSDE when we refer to a single object. With the term stability we understand the continuity of the operator that maps the standard data of a BSDE, a set which among others includes the terminal value of the BSDE and the filtration with respect to which the solution has to be adapted, to its solution. In other words, the stability property allows to obtain an approximation of the solution of the BSDE under interest, once we determine an approximation of the standard data of the BSDE under interest. In this thesis we provide a general wellposedness result of multidimensional BSDEs with stochastic Lipschitz generator and which is driven by a possibly stochastically discontinuous square-integrable martingale. The time horizon can be infinite and as already implicitly has been stated, the right-continuous filtration is allowed to be stochastically discontinuous. Moreover, we provide a framework under which the stability property of BSDEs is verified. This framework allows for both continuous-time and discrete-time L2 −type approximations, which can turn out to be particularly useful for the well-posedness of numerical schemes for BSDEs. These results are presented in the second and the fourth chapter of this thesis. In the third chapter the stability of martingale representations is obtained, a result which lies at the core of the stability property of BSDEs. The property of the stability of martingale representations is not only a useful tool for our current needs, but it is also an interesting result on its own. Roughly speaking, it amounts to the convergence o…
author: Saplaouras, Alexandros
language: en
license: https://creativecommons.org/licenses/by-nc-sa/4.0/
date published: 2017
date modified: 2026-07-27T21:28:37Z
provider: Technische Universität Berlin
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Technische Universität Berlin

PropertyValue
property ID: DOI
value: 10.14279/depositonce-6154