Abstract
Based on the mean-variance portfolio selection under multi-period criterion, this paper focuses on the study of the uncertain time horizon and the regime-switching market including the bankruptcy state, where the conditional distribution of exit time is followed by the market state. When the market enters the bankruptcy state, investors are assumed to get back δ part of the wealth from the bankrupt company, where δ refers to the retrieval rate. By introducing the Lagrange multiplier λ, we create an innovative expression for the wealth process and the iterative representation of the value function to obtain the analytical expression of the optimal strategy and the corresponding efficient frontier. Besides, some special cases and numerical examples are presented to demonstrate the effects of state-dependent exit probability and bankruptcy state on the investment strategy.
Highlights
Since the precursory research of Markowitz [1], the mean-variance (MV) criterion has become the most commonly used theoretical assumption and basis in portfolio selection and has been extended to many different kinds of applications
Based on the mean-variance portfolio selection under multi-period criterion, this paper focuses on the study of the uncertain time horizon and the regime-switching market including the bankruptcy state, where the conditional distribution of exit time is followed by the market state
Because of this novel research angle in this paper, the wealth process becomes fairly different from previous formulations, and we assume that the conditional exiting probability depends on the current market state including the bankruptcy state
Summary
Since the precursory research of Markowitz [1], the mean-variance (MV) criterion has become the most commonly used theoretical assumption and basis in portfolio selection and has been extended to many different kinds of applications. Based on the above consideration, we cannot predetermine the state-dependent time horizon since the market state is unknown prior to the corresponding time point, which suggests that this assumption is different and much more realistic than those in the existing literature Because both the bankruptcy state and the statedependent investment time horizon often occur in the real world, it is significant. Wu et al [19] assumed that the uncertain time horizon depends on the market state, the exit probability is not considered Because of this novel research angle in this paper, the wealth process becomes fairly different from previous formulations, and we assume that the conditional exiting probability depends on the current market state including the bankruptcy state.
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