Time-consistent and self-coordination strategies for multi-period mean-Conditional Value-at-Risk portfolio selection

The multi-period mean-Conditional Value-at-Risk (mean-CVaR) portfolio decision model is prone to time inconsistency problems that drive CVaR investors away from the pre-committed portfolio strategy, although this strategy is regarded as the global optimal strategy at the initial time point. In the existing literature, authors have proposed time-consistent and self-coordination strategies to solve the time inconsistency issue arising from other sequential decision problems. However, these strategies are rarely studied under the multi-period mean-CVaR portfolio decision framework. This work fills in these gaps by providing both computationally tractable methods and analytical solutions for these strategies. The revealed time-consistent strategy is a piecewise linear function of the wealth level, wherein the other parameters can be computed by solving a series of mixed-integer programming problems off line. The self-coordination strategy can be formulated as a convex program with a quadratic constraint. We also prove that the pre-committed strategy and the time-consistent strategy are the extreme cases of the self-coordination strategy. Furthermore, we extend our main findings to a regime-switching market setting.