在部分信息下股票收益服从隐马尔科夫模型的最优交易策略

摘要

An optimal trading strategy is characterized under partial information with the dividend payment. A multi-stock market model is considered where prices satisfy a stochastic differential equation with instantaneous rates of return modeled as a continuous time Markov chain with finitely many states. For the investor's objective of maximizing the expected utility of the terminal wealth, an explicit representation of the optimal trading strategy is derived by using hidden Markov models (HMM) filtering theory and Malliavin calculus.%讨论了部分信息下股票支付红利的最优交易策略.考虑一个多种股票模型,股票价格过程满足随机微分方程,股票价格的瞬时收益率由有限状态连续时间的马尔科夫链刻画.在投资者终端财富预期效用最大化目标下,利用隐马尔科夫模型(HMM)滤波理论和Malliavin分析,导出最优交易策略的显式表达式.