OPTIMAL CONTROL OF MARKOVIAN SWITCHING SYSTEMS WITH APPLICATIONS TO PORTFOLIO DECISIONS UNDER INFLATION

This article is concerned with a class of control systems with Markovian switching, in which an It5 formula for Markov-modulated processes is derived. Moreover, an optimal control law satisfying the generalized Hamilton-Jacobi-Bellman （HJB） equation with Markovian switching is characterized. Then, through the generalized HJB equation, we study an optimal consumption and portfolio problem with the financial markets of Markovian switching and inflation. Thus, we deduce the optimal policies and show that a modified Mutual Fund Theorem consisting of three funds holds. Finally, for the CRRA utility function, we explicitly give the optimal consumption and portfolio policies. Numerical examples are included to illustrate the obtained results.

基于随机基准的三基金定理动态决策模型

在Black-Scholes型金融市场下,通过一个随机过程来定义基准,以低于基准的不足概率作为风险约束,以最大化期望相对终端财富为决策目标,构建了动态投资组合决策模型,并给出了最优投资策略和有效前沿的显式表达式。结果表明:最优投资策略由无风险资产,修正的市场组合及“基准组合”构成,可视为三基金定理。最后给出了数值例子。

基于内幕信息的资产市场一般跨期均衡模型

研究了资产市场的一般跨期均衡问题,通过对知情交易者和非知情交易者的需求分析,讨论存在内幕信息情况下的市场需求情况,从而给出了市场出清时的均衡条件和内幕信息情况下的三"基金"分离定理。结果显示,资产市场的均衡随内幕信息的变化而变化,并受知情交易者占总交易者比例的影响;当无风险利率为常数时,通过市场均衡条件给出了存在内幕信息情况下的证券市场线,发现内幕信息是资产收益的一个影响因子。