On the Wellposedness of Forward-Backward SDEs— A Unified Approach
Speaker:Prof. Zhen Wu
School of Mathematics
Shandong University
Date & Time:20 Feb 2013 (Wednesday) 15:00
Venue:U102
Organized by:Department of Mathematics

Abstract

The theory of Backward Stochastic Differential Equations (BSDEs) and Forward-Backward SDEs (FBSDEs) has been extensively studied for the past two decades, and its applications have been found in many branches of applied mathematics, especially the stochastic control theory and mathematical finance. The option pricing problem in the financial market and the celebrated principal-agent problem can be formulated as the forward-backward stochastic differential equations. It has been noted, however, that while in many situations the solvability of the original problems is essentially equivalent to the solvability of certain type of FBSDEs, these (mostly non-Markovian) FBSDEs are often beyond the scope of any existing frameworks.

In this talk, I will present our main result on the wellposedness of FBSDEs in a general non-Markovian framework. The main purpose is to build on all the existing methodology in the literature, and put them into a unified scheme. Our main device is a decoupling random field, and its uniform Lipschitz continuity in the spatial variable is crucial for the wellposedness of the original FBSDE. By analyzing a characteristic BSDE, which is a backward stochastic Riccati equation with quadratic growth in the Z component, we find various conditions under which such decoupling random field exists, which lead ultimately to the solvability of the original FBSDEs.

Biography

Prof. Zhen Wu is currently a Vice Dean and Professor of School of Mathematics and System Science of Shandong University. Prof. Wu obtained his Ph.D. in Applied Mathematics in Shandong University as well. He is interested in Optimal Control, Probability and Financial Mathematics. Prof. Wu received various awards, such as, The Second Prize of Excellent Teaching achievement of Shandong Province, The Eighth youth scientific price of Shandong Province, and The Second Prize of National Teaching achievement of China. The publication of Prof. Wu include, Maximum principle for optimal control problems of forward–backward regime-switching system and applications, Backward stochastic viability and related properties on Z for BSDEs with applications, Maximum Principle for Stochastic Recursive Optimal Control Problems Involving Impulse Controls, Corporate optimal investment under incomplete information: a real option method etc.