Minimization of risks in pension funding by means of contributions and portfolio selection

We consider a dynamic model of pension funding in a defined benefit plan of an employment system. The prior objective of the sponsor of the pension plan is the determination of the contribution rate amortizing the unfunded actuarial liability, in order to minimize the contribution rate risk and the solvency risk. To this end, the promoter invest in a portfolio with n risky assets and a risk-free security. The aim of this paper is to determine the optimal funding behavior in this dynamic, stochastic framework.