|
Backward Stochastic Differential Equations:
Feb 14, 2001
|
| Abstract: Backward stochastic differential equation (BSDE) and its generalized form, Forward-backward stochastic differential equation (FBSDE), have received strong attention in the past decade because of their interesting structures and their usefulness in various applied fields, most notably mathematical finance. In this talk I will introduce the origin of the BSDE and some basics of the theory, and then give a survey of finance problems where BSDEs have proved to be useful. These problems will include, but not limited to: option pricing, optimal hedging (for small or large investors), portfolio optimizations, stochastic recursive utilities, term structure of interest rates, stochastic Black-Scholes formula, path regularity of optimal hedging, and some numerical aspects of Black-Scholes formula. The relations among BSDEs, FBSDEs, PDEs, Stochastic PDEs, and Backward Stochastic PDEs will be illustrated as well. |
©
2001 Purdue University Last Update: July 10, 2001 Please send comments and suggestions to the Webmaster. |