Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund

Abstract This paper deals with the pension fund management issue. We focus on defined-contribution plans where a guarantee is given on the benefits, and the guarantee depends on the level of the stochastic interest rate when the employee retires. It is particularly shown that the optimal composition of this kind of pension fund can be divided into three different parts: a loan which amounts to the present value of the contributions, a contingent claim delivering the guarantee and a hedging fund. A Vasicek interest rate model is considered as an illustration of our analysis.

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