随机动态系统的风险分析及其最优控制问题

项目名称： 随机动态系统的风险分析及其最优控制问题

项目编号： No.11471341

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 黄永辉

作者单位： 中山大学

项目金额： 72万元

中文摘要： 马氏决策过程(MDP)是一类随机动态系统的最优控制理论，适合分析和解决许多实际问题，近年来得到广泛的关注和研究, 是随机最优控制领域的热门分支。本项目将基于最优控制和随机动态系统理论的最新成果，研究具有丰富实际背景和应用意义的连续时间参数MDP的风险分析和最优控制问题，考虑有限阶段损失、无限阶段折扣损失、首达目标损失和长期平均损失的风险分析及其优化，风险准则主要包括：VaR，AVaR,一致风险测度和风险灵敏准则等。研究内容有：（1）风险最优策略的存在性、结构和特征；（2）风险最优策略的计算方法；（3）具体实际模型的计算机模拟和应用。本项目上述研究内容具有前沿性、开创性和实用性，完成这些研究内容将推动随机最优控制理论的新进展。

中文关键词： 随机优化；随机最优控制；随机模型

英文摘要： Markov decision processes (MDP) form an important class of optimal control theory for stochastic dynamic systems. Since such a kind of stochastic models can analyze and solve many practical problems, they receive extensive attentions and studies in recent years, which are in fact a hot branch in the area of stochastic optimal control nowadays. Based on the recent developments on the theory of optimal control and stochastic dynamic systems, this project aim to study risk analysis and optimal control problems for continuous-time MDP with finite horizon loss,infinite horizon discounted loss，first passage loss and long-run average loss. The risk measures mainly include VaR, AVaR, coherent risk measure, and risk-sensitive criteria. The research contents are as follows; (1) the existence, the structure and the characteristic of risk optimal policies under various risk measures; (2)the algorithms for computing risk optimal policies under various risk measures; (3)the simulations and the applications of the developed results to practical problems. The research contents above are advanced, initiative and practical. By the accomplishment of this research, the theory of stochastic optimal control will make new progress.

英文关键词： stochastic optimization;stochastic optimal control;stochastic models