Time-Consistent Investment and Contribution Adjustment Strategies for a Multi-Cohorts Db Pension Plan Under Smooth Ambiguity Utility

Abstract

In this paper, we consider the optimal investment and contribution adjustment problem for a multi-cohorts DB pension plan in an environment with parameter uncertainty. Preferences towards risk and ambiguity are modeled using the smooth ambiguity approach. Since the pension trustee is ambiguous about the risky assets, she/he decides to invest in a risk-free asset, a purely risky asset and an ambiguous risky asset whose return is uncertain. The objective is to maximize the expectation of the accumulated adjusted discount contribution and discount terminal wealth under a smooth ambiguity utility which is the double power form. The utility function makes the problem time-inconsistent and we establish the extended HJB equation via game theoretic formulation. The optimal equilibrium strategy and equilibrium value function are derived under smooth ambiguity. Finally, sensitivity analysis of equilibrium strategy is presented to demonstrate the effects of model parameters on the equilibrium strategy.

Keywords: DB pension plan, Multi-cohorts structure, Smooth ambiguity utility, Time-consistent strategy, Equilibrium control law