随机微分博弈及其应用研究

项目名称： 随机微分博弈及其应用研究

项目编号： No.11271375

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 林祥

作者单位： 浙江工商大学

项目金额： 60万元

中文摘要： 本项目拟利用随机最优控制理论系统研究随机微分博弈理论及其在医学治疗、投资组合和再保险中的应用。运用动态规划原理(HJB方程)，鞅方法，最大值原理，以及随机线性二次控制技巧解决扩散和跳项中含策略的主从零和随机微分博弈和合作微分博弈的最优策略选择问题，得到目标值函数，损益分布方案以及最优策略的显示表达式或所满足的方程。通过数值计算和随机模拟，找到目标值函数和最优策略与模型主要参数之间的关系，并给出相应的经济分析。同时，把所得理论结果应用到医学治疗、投资组合和再保险选择等实际问题中。该项目所研究的问题是现代博弈理论中的最新热点研究问题，是博弈论、随机最优控制以及数理金融等领域的交叉研究。该项目的研究将极大的促进随机微分博弈，随机最优控制和数理金融等理论和应用的发展。

中文关键词： 零和随机微分博弈；非零和随机微分博弈；纳什均衡；HJB方程；数值计算

英文摘要： We study the theory of stochastic differential game and its application to medical treatment，portfolio selection and reinsurance by using the stochastic optimal control theory. We discuss the leader-follower zero-sum stochastic differential game and cooperative stochastic differential game under that the control(strategy) enters into the diffusion and jump of the system. By invoking the use of the dynamic programming approach (HJB equation), martingale methods, the maximum principle, the stochastic linear-quadratic control approach, we aim to obtain the closed-form solutions or the equations for the value function, payoff distribution procedure as well as the optimal strategy. We provide some numerical examples and stochastic simulation to illustrate how the value function, payoff distribution procedure and the optimal strategy change when the model parameters vary. We also give some economic analysis. We apply the result of stochastic differentail game to the practical medical treatment, portfolio selection and reinsurance. The problem of this project is one of the central issues in the theory and practice of modern game theory. The research of this project will greatly promote the stochastic differential game, stochastic optimal control and mathematical finance theory and application development.

英文关键词： zero-sum stochastic differential game；non-zero sum stochastic differential game；Nash equilibrium；HJB equation；numerical calculus