Determination of Optimal Contribution Rate and Optimal Investment Portfolio of Defined Benefit Pension Plan Under the Expected Shortfall Constraint

Abstract

We establish stochastic models considering stochastic growth rate of salary, stochastic return rate of investment portfolio and stochastic mortality to evaluate pension surplus. We also establish the stochastic objective function of minimizing the contribution rate satisfying the constraint of expected shortfall less than a constant. We consider the time varying of means and variance of return rate of investment and deduct the calculation formula of time varying covariance of it. We apply the Monte Carlo simulation, and stochastic optimization techniques with the help of Matlab to find the optimal solutions of contribution rate and investment portfolio. Finally, we discuss the effect of the changes of the age of participating pension plan, the retirement age and mortality improvement on the optimal contribution rate and the effect of changing retirement age on the replacement rate.