Robust strategy for a member of defined contribution pension plan when asset prices can jump

Abstract

This paper investigates the robust optimal investment for an ambiguity averse member of a defined contribution (DC) pension plan in a fully-fledged, time consistent mean-variance modeling framework. In particular, the paper extends the literature on defined contribution pension plans in three directions: (1) We relax its assumption of purely continuous stock and/or contribution processes, which allows to introduce the effects of news, job loss, macroeconomic conditions, etc., into the model; (2) Unlike most studies in DC pension plans, we allow for ambiguity about both the mean arrival rate and jump size distribution of the stock returns and contribution rate processes of the member; (3) Ambiguity in our setting is time-varying. The model thus features stochastic stock volatility, stochastic interest rate, stochastic contribution rate, jumps in both stock and contribution rate processes, and time-varying ambiguity about diffusion parameters. Welfare analysis indicates that ignoring ambiguity can be very costly to the member. The framework proposed in this paper is general and adds significant realism to existing models in the literature.