主 题: 北大金融数学系20周年系庆系列报告 A-7——A Primal-Dual Iterative Monte Carlo Method for Stochastic Dynamic Programs and Its Applications in Finance
报告人: 陈南 副教授 (香港中文大学系统工程与工程管理系)
时 间: 2017-04-14 14:00-15:00
地 点: 理科一号楼1560
【报告摘要】： Stochastic dynamic programming is a technique for modelling and solving problems of sequential decision making under uncertainty. It finds a wide range of applications in economics, finance, and operations research. The convention wisdom is to make use of the Bellman equation to achieve optimality by trading off the immediate rewards and the long-term impact of actions. Despite its mathematical elegancy, the feasibility of the Bellman equation is largely limited due to the computational intractability caused by the problem dimensionality. Therefore, we have to rely on heuristics on many occasions to solve large-scaled SDP problems.
In this paper we use the information relaxation technique to propose a new value-and-policy iterative method to tackle these problems. Each iteration generates a confidence interval estimate for the true value function and a corresponding sub-optimal policy so that we can use the gap between the upper and lower bounds to access the quality of the current policy. We show that the resulted sequences of suboptimal policies will converge to the optimal one within a finite number of iterations.
A regression-based Monte Carlo algorithm is introduced to overcome the dimensionality curse in the implementation of this approach for high dimensional cases. Our formulation reduces the original problem to solving a sequence of open loop control problems. We can thereby leverage on a variety of well-developed deterministic optimization algorithms to accelerate the computational speed. That differentiates our method from the traditional literature of approximate dynamic programs in which a majority of methods need to solve stochastic optimization problems. As numerical illustrations, we apply the algorithm to the optimal order execution problem and the portfolio selection problems. Some new insights about optimal value and optimal policy are also discussed.
报告人简介：
陈南 副教授，香港中文大学系统工程与工程管理系
陈南教授分別于1998年和2001年获得北京大学概率概率统计专业学士学位和硕士学位，并于2006年获得哥伦比亚大学运筹学专业博士学位。2006年获得INFORMS 金融服务领域最佳学生论文二等奖。 其研究兴趣包括金融风险管理中的定量方法，蒙特卡洛模拟和应用概率。有十余篇文章发表在 Review of Financial Studies, Operations Research, Mathematics of Operations Research, Mathematical Finance, Finance and Stochastics 等运筹和数理金融领域的顶级期刊上。陈教授之前的研究课题涵盖信用利差模型，可转换证券定价的随机微分博弈，美式期权定价的蒙特卡洛方法及其敏感性分析，随机微分方程模拟，跳扩散模型中的奇异期权定价。目前，他主要关注于系统性传染和流动性风险的建模，应急可转债合约中的激励问题，复杂的社交和金融网络，以及蒙特卡洛方法在随机控制和学习中的应用。他的部分研究得到了香港研究资助局优配研究金的资助 (六次)。
陈南教授于 2007-2008年担任Operations Research Letters的副编辑，并且参与了多次定量金融和蒙特卡洛模拟领域的国际学术会议的组织工作。同时担任香港中文大学深圳校区金融工程理学硕士项目副主管和香港中文大学工程学院金融科技（FinTech）工程学学士课程主管。
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