Mean–variance portfolio and contribution selection in stochastic pension funding

In this paper we study the problem of simultaneous minimization of risks, and maximization of the terminal value of expected funds assets in a stochastic defined benefit aggregated pension plan. The risks considered are the solvency risk, measured as the variance of the terminal fund’s level, and the contribution risk, in the form of a running cost associated to deviations from the evolution of the stochastic normal cost. The problem is formulated as a bi-objective stochastic problem of mean–variance and it is solved with dynamic programming techniques. We find the efficient frontier and we show that the optimal portfolio depends linearly on the supplementary cost of the fund, plus an additional term due to the random evolution of benefits.