隐半马尔科夫市场下投资组合的动态决策问题（英文）  

Dynamic Portfolio Decision Under the Hidden Semi-Markov Market

作　　者：何其祥 HE Qixiang(School of Mathematics,Shanghai University of Finance and Economics, Shanghai 200433,China;Zhejiang College,Shanghai University of Finance and Economics,Jinhua 321013,China)

机构地区：[1]上海财经大学数学学院,上海200433 [2]上海财经大学浙江学院,浙江金华321013

出　　处：《应用数学》2019年第1期45-62,共18页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11671097)

摘　　要：在长期投资组合中,既要考虑金融资产自身的价格波动风险,又要关注宏观经济环境变化及通胀风险对各资产的影响.为此,本文建立宏观经济环境服从隐半马尔科夫链的金融市场,由通胀指数债券、银行存款和普通股票构成投资组合.由期望效用最大化构建随机控制模型,考虑到该隐半马尔科夫市场的不完备性,进一步将该投资组合问题视作部分信息的随机控制问题,并利用隐半马尔科夫滤波将部分信息控制问题转化问完全信息问题,得到解的存在唯一性.本文最后给出若干数值模拟结果,结果显示本文建立的模型优于普通市场的模型.In a long-term investment process, we need to consider the financial risk of asset itself, and the influence on portfolio taken by economic environment and inflation risk.A dynamic decision of a portfolio in a hidden semi-Markov model(HSMM) is investigated in this paper. We construct a financial market in which the macroeconomic environment is driven by a hidden semi-Markov chain. In this market, there is an inflation index bond, a bank account and stock. A stochastic control problem by maximizing the expected utility is studied. Considering the market is incomplete, we regard this problem as a stochastic optimal control with partial information one. In order to solve it, HSMM-filtering is proposed. The partial information problem is converted into a complete one. By using the dynamic programming approach, a regime-switch Hamilton-Jacobi-Bellman(HJB) is derived. At last, numerical and sensitivity analysis are provided. From the numerical results, the model under HSMM performs better than the traditional portfolio model.

关 键 词：长期投资组合 隐半马尔科夫链 最优随机控制 

分 类 号：O211.60[理学—概率论与数理统计] O231.3[理学—数学]