Time-Consistent Portfolio Selection for Rank-Dependent Utilities in a Constrained Market
研究了在投资策略受限于闭凸集的市场中，具有等级依赖效用的投资者的时间一致投资组合选择问题，刻画了确定性严格均衡策略并分析了其存在性与求解方法。
We investigate the portfolio selection problem for an agent with rank-dependent utility, for which the investment strategy is constrained to take values in a closed convex set. For a constant coefficient market and constant relative risk-aversion utilities, we characterize the deterministic strict equilibrium strategies. For the case of time-invariant probability weighting functions, we provide a comprehensive characterization of the deterministic strict equilibrium strategy. The unique nonzero equilibrium, if it exists, can be determined by solving an autonomous ordinary differential equation (ODE). In the case of time-varying probability weighting functions, we observe that there may be infinitely many nonzero deterministic strict equilibrium strategies, which are derived from the positive solutions to a nonlinear singular ODE. By specifying the maximal solution to the singular ODE, we are able to identify all the positive solutions. In addition, we address the issue of selecting an optimal strategy from the numerous equilibrium strategies available. Funding: This research was supported by the National Key R&D Program of China [Grant 2020YFA0712700] and the National Natural Science Foundation of China [Grants 12431017, 12471447, 11971301].