讲座简介：

上半场：

主讲人：葛浩

时间：2018年5月21日2:20pm-4:20pm

地点：善衡堂N122

主题：不确定投资期下带马尔可夫机制转换及随机现金流的多期均值-方差投资组合选择问题的均衡解

下半场：

主讲人：陈南（香港中文大学副教授）

时间：2018年5月21日4:30pm-6:00pm

地点：善衡堂N122

主题：A confidence Interval-based learning method for stochastic dynamic programs and its applications

摘要：

Stochastic dynamic programs find various applications in economics, finance, and operations management. The solution offers insights on how to make decisions in a stochastic environment. However, the traditional Hamilton-Jacobi-Bellman equation based approaches suffer from the “curse of dimensionality” when the spaces of state, randomness, and actions of the problem are all of high dimensions. On numerous occasions people therefore have to rely on approximate heuristic policies to maintain computational tractability. That necessitates the investigation of the following two research problems: 

1. How can we assess the quality of a given policy? 

2. If we know the performance of a policy is not satisfactory, do we have a systematic way to improve it? 

To address these two problems, we employ the information relaxation technique in this paper to develop a method of value iteration to solve SDP. The advantages of the new method are that we can construct valid confidence interval to assess the performance of a heuristic policy and provide a recursive improvement scheme. 

Our formulation reduces the original problem to solving a sequence of open loop control problems. We can thereby rely on a variety of well-developed deterministic optimization algorithms, such as difference-of-convex-function programs, to accelerate the computational speed. Our approach is different from the traditional literature of approximate dynamic programs in which a majority of methods need to solve stochastic optimization problems. Monte Carlo simulation is used to overcome the dimensionality curse in the learning of value functions for high dimensional cases. As numerical illustrations, we apply the algorithm to the optimal order execution problem and an inventory management problem with lead time. Some new insights about optimal value and optimal policy are also discussed. The method can also be extended to the cases with model uncertainty.

主讲人简介：

Nan Chen is an associate professor in the Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong. His research interests are quantitative methods in finance and risk management, Monte Carlo simulation, and applied probability. He has published in top journals and referred conference proceedings in the fields of operations research and quantitative finance, such as Review of Financial Studies, Operations Research, Mathematics of Operations Research, Mathematical Finance, Finance and Stochastics, Journal of Economic Dynamics and Control.

Nan Chen received his Ph.D. in operations research from Columbia University in 2006, and M.S. and B.S. in probability and statistics from Peking University, Beijing, China in 2001 and 1998, respectively. He served as associate editor for Operations Research Letters from 2007-2008 and chaired (or was a member of) the program committees of several international conferences on quantitative finance and Monte Carlo simulation. He now serves as director of the Bachelor of Engineering Program in Financial Technology at CUHK. The program is the first of its kind in Hong Kong to offer comprehensive undergraduate education in FinTech. He is also deputy director of Master of Science Program in Financial Engineering at CUHK Shenzhen.