Robust equilibrium control-measure policy for a DC pension plan with state-dependent risk aversion under mean-variance criterion

Abstract

<p style='text-indent:20px;'>In reality, when facing a defined contribution (DC) pension fund investment problem, the fund manager may not have sufficient confidence in the reference model and rather considers some similar alternative models. In this paper, we investigate the robust equilibrium control-measure policy for an ambiguity-averse and risk-averse fund manger under the mean-variance (MV) criterion. The ambiguity aversion is introduced by adopting the model uncertainty robustness framework developed by Anderson. The risk aversion model is state-dependent, and takes a linear form of the current wealth level after contribution. Moreover, the fund manager faces stochastic labor income risk and allocates his wealth among a risk-free asset and a risky asset. We also propose two complicated ambiguity preference functions which are economically meaningful and facilitate analytical tractability. Due to the time-inconsistency of the resulting stochastic control problem, we attack it by using the game theoretical framework and the concept of subgame perfect Nash equilibrium. The extended Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations and the verification theorem for our problem are established. The explicit expressions for the robust equilibrium policy and the corresponding robust equilibrium value function are derived by stochastic control technique. In addition, we discuss two special cases of our model, which shows that our results extend some existing works in the literature. Finally, some numerical experiments are conducted to demonstrate the effects of model parameters on our robust equilibrium policy.