Dynamic Liability-Driven Investment under Sponsor’s Loss Aversion

Abstract

This paper investigates a dynamic liability-driven investment policy for defined-benefit (DB) plans by incorporating the loss aversion of a sponsor, who is assumed to be more sensitive to underfunding than overfunding. Through the lens of prospect theory, we first set up a loss-aversion utility function for a sponsor whose utility depends on the funding ratio in each period, obtained from stochastic processes of pension assets and liabilities. We then construct a multi-horizon dynamic control optimization problem to find the optimal investment strategy that maximizes the expected utility of the plan sponsor. A genetic algorithm is employed to provide a numerical solution for our nonlinear dynamic optimization problem. Our results suggest that the overall paths of the optimal equity allocation decline as the age of a plan participant reaches retirement. We also find that the equity portion of the portfolio increases when a sponsor is less loss-averse or the contribution rate is lower.