Multiperiod Mean-CVaR Portfolio Selection

Due to the time inconsistency issue of multiperiod mean-CVaR model, two important policies of the model with finite states, the pre-committed policy and the time consistent policy, are derived and discussed. The pre-committed policy, which is global optimal for the model, is solved through linear programming. A detailed analysis shows that the pre-committed policy doesn't satisfy time consistency in efficiency either, i.e., the truncated pre-committed policy is not efficient for the remaining short term mean-CVaR problem. The time consistent policy, which is the subgame Nash equilibrium policy of the multiperson game reformulation of the model, takes a piecewise linear form of the current wealth level and the coefficients can be derived by a series of integer programming problems and two linear programming problems. The difference between two polices indicates the degree of time inconsistency.