Backward stochastic differential equations and applications in finance: numerical methods

Abstract

This post-graduate thesis deals with the subject of backward Stochastic Differential Equations (BSDEs), with applications in financial and numerical algorithms for solving these equations. The BSDEs are stochastic differential equations equipped with a terminal border condition. BSDEs have been studied extensively over the last decade. BSDEs appear in financial and stochastic control problems. Regarding applications in finance, BSDEs mainly appear in option theory. Before presenting the BSDEs, a reference to key points of stochastic integration by Ito and useful theorems, will be presented. After the presentation of Ito theory, an introduction to the basic theory of BSDEs and the existence and uniqueness theorems of the solution, follow. The next step is to present a numerical algorithm to solve BSDEs and the implementation code in R language. Finally, some simple examples of solution will be adapted, as applications of the developed code.