隐Markov 机制转移与随机时间水平下的多期资产配置*

Multi-period Portfolio Selection with Hidden Markov Regime Switching and Stochastic Investment Horizon

在状态部分可观测的金融市场中,研究了投资活动终止时间不确定的多阶段均值-方差投资组合选择问题。假定市场存在有限个不可观测状态,利用离散时间时变隐Markov链描述不可观测状态的变化过程;无风险资产在各个阶段的收益率依赖于可观测市场状态;风险资产在各阶段的收益率同时依赖于可观测和不可观测市场状态。通过构造充分统计量,部分信息下的投资组合选择问题等价地转化为了完全信息下的优化问题。再利用动态规划方法和拉格朗日对偶原理,得到了最优资产组合策略和有效边界的解析表达式。

A multi-period mean-variance portfolio selection problem with stochastic investment horizon in the financial market where the market states are partially observable is considered. Suppose that the dy- namics of the unobservable market states is described by a finite-state discrete-time hidden Markov chain. Return of the risk-free asset is assumed to depend on the observable market state at that period. And re- turn of the risky asset is assumed to be dependent both on the observable and unobservable market states at that period. The portfolio selection optimization problem with partially observable information is trans- formed into the optimization problem with fully observable information by using the method of sufficient statistics. And explicit expressions of optimal portfolio strategy and efficient frontier are derived by adopting dynamic programming approach and Lagrange dual theory.