BFS 2002

Poster Presentation

We consider a continuous time dynamic model of pension funding in a defined-benefit plan of an employment system. The benefits liabilities are random, given in the general case for a path-continuous Ito process. Three different situations are studied regarding the investment decisions taken by the sponsoring employer: In the first one the fund is invested at a constant and risk-free rate of interest; in the second one the promoter invest in a portfolio with n risky assets and a risk-free security; finally, it is supposed that the rate of return is stochastic. Modelling the preferences of the manager such that her or his main objective is to minimize both the contribution rate risk and the solvency risk, we find that the optimal behavior leads to a spread method of funding. This is achieved with a natural selection for the force of interest used to value the actuarial functions intervening in the design of the pension plan. The aim of this paper is to determine the optimal funding behavior in this stochastic, continuous time framework, over an unbounded horizon.