江苏师范大学
江苏高校优势学科概率统计前沿系列讲座之四十四
报 告 人：许顺吉教授
报告题目：On HJB Equations for Consumption Problems
报告时间：2015年4月26日（周日下午3:30）
报告地点：江苏师范大学数学与统计学院学术报告厅（静远楼1506室）
主办单位:数学与统计学院、科技处
报告摘要：
Merton-type optimal consumption problems are classical portfolio optimization problems. There is a huge literature addressing the problem, although its study is still far from complete. We can view the problem as a stochastic control problem. The dynamic programming is a standard approach used in the control theory, which leads to the Hamilton-Jacobi-Bellman equation (HJB). When the HJB equation can be solved, a candidate of (Markovian) optimal consumption policy can be derived. This approach suggests that an optimal consumption problem can be solved through a study of a nonlinear partial differential equation (elliptic type or parabolic equation), hence a need for a serious study of HJB equation.
In this note, we consider the general factor models as an example to show some calculation based on HJB equation and martingale method. The first part is a calculation for complete market. In the second part we consider incomplete market. The use of “fictitious” completion in martingale leads to a game interpretation of HJB equation. This suggests a solution of HJB equation by choosing a direction to the saddle point (of the game problem). This reduces the problem to the problems on a sequence of complete markets. The convergence will be discussed. The idea may have practical use to construct approximation of optimal portfolio. The discussions relate to recent studies of Rogers (2003), Rogers- Zaczkowski (2013). The talk is based on joint works with Hata (2012), Hata-Nagai-Sheu (2015) and an ongoing project of Fleming-Nagai-Sheu.
许顺吉教授简介：
Shuenn-Jyi Sheu received B.S. from Department of Mathematics, National Central University in 1975 and M.S. from National Taiwan University in 1977. In 1979, he came to Brown University for the graduate study in Mathematics and received his Ph.D. in 1982. Afterward he was a visiting assistant professor in the Division of Applied Mathematics, Brown University for one year. In 1983, he joined the Institute of Mathematics, Academia Sinica as an Associate Research Fellow. From 1986, he is a Research Fellow .
Dr. Sheu major research interest is the applications of stochastic analysis. In the past few years, he has done some works on the problems related to the large deviation theory as well as on the use of control method to study the problems related to Markov processes including diffusion processes. He also works on some mathematical problems arised from Monte Carlo method. He has nearly 50 publications in Ann. Probab.，Ann. Appl. Probab.，Math. Finance，Probab. Theory Related Fields，SIAM J. Math. Anal.，SIAM J. Control Optim.，Appl. Math. Optim.，Trans.， Amer. Math. Soc..