機率研討會

主講者: Profesor Huyen Pham (University Paris 7, France)
講題: Stochastic Control and Aplications in Finance - Lecture 3: BSDEs and stochastic control
時間: 2010-06-02 (Wed.)  14:00 - 15:30
地點: 數學所 722 研討室 (台大院區)
Abstract:

The aim of these lectures is to present an introduction to stochastic control, a classical topic in applied mathematics, which has known important developments over last few years inspired especially by problems in mathematical finance. We give an overview of the main methods and results in this area.

We first present the standard approach by dynamical programming principle and verification theorem, and point out the limits of this method. We then move on to the viscosity solutions approach: it requires more theory and technique, but provides the general mathematical tool for dealing with stochastic control in a Markovian context. The last lecture is devoted to an introduction to the theory of backward stochastic differential equations (BSDEs), which has emerged as a major research topic with significant contributions in relation with stochastic control beyond the Markovian framework.

The various methods presented in these lectures will be illustrated by several applications arising in economics and finance. We also give a short outlook over some extensions and open problems.


References
H. Pham (2009), Continuous time stochastic control and optimization with finance applications, Series SMAP, Springer.
I. Kharroubi, J. Ma, H. Pham and J. Zhang (2010), Backward stochastic differential equations with constrained jumps and quasi-variational inequalities, Ann. Probab., Vol. 38, 794-840.
 
  || Close window ||