讲座题目：Stochastic Optimization in Finance and DC Pension Funds

时间：2018年11月15日（星期四）13:00-14:30

地点：博识楼434

报告人：Dr. Aihua Zhang（Department of Mathematics, University of Leicester）

报告简介：The continuous-time intertemporal consumption-portfolio optimization problem was pioneered by Merton (1969, 1971), using the method of dynamic programming. In the 1980s, Karatzas et al (1986), Pliska (1986) and Cox/Huang (1989) developed an alternative approach, the Martingale method, to the continuous-time problem. Certainly the economic literature is dominated by the stochastic dynamic programming approach, which has the advantage that it identifies the optimal strategy automatically as a function of the underlying observables, which is sometimes called feedback form. However, it often turns out that the corresponding Hamilton-Jacobi-Bellman equation, which in general is a second order non-linear partial differential equation, does not admit a closed-form solution. In contrast, by utilizing the Martingale method, a closed-form solution can be obtained without solving any partial differential equation in many specific models when asset prices follow a geometric Brownian motion. 

This talk will give an overview of the stochastic optimization problems in various situations with the aid of the Martingale method. The optimal investment problems will be discussed under the situations, where an inflation risk is presented, where the investors need to invest in a DC pension fund, and where the financial market is incomplete. I will briefly explain how to solve/deal with the stochastic optimization problems under such situations in turn.