Mean-variance investment and contribution decisions for defined benefit pension plans in a stochastic framework

Abstract

In this paper we investigate the management of a defined benefit pension plan under a model with random coefficients. The objective of the pension sponsor is to minimize the solvency risk, contribution risk and the expected terminal value of the unfunded actuarial liability. By measuring the solvency risk in terms of the variance of the terminal unfunded actuarial liability, we formulate the problem as a mean-variance problem with an additional running cost. With the help of a system of backward stochastic differential equations, we derive a time-consistent equilibrium strategy towards investment and contribution rate. The obtained equilibrium strategy turns out to be a good candidate for a stable contribution plan. When the interest rate is given by the Vasicek model and all other coefficients are deterministic, we obtain closed-form solutions of the equilibrium strategy and efficient frontier.