Mean-variance target-based optimisation in DC plan with stochastic interest rate

We solve a mean-variance optimisation problem of a defined contribution pension scheme in the accumulation phase. The financial market consists of: (i) the risk-free asset, (ii) a risky asset following a GBM, and (iii) a bond driven by a stochastic interest rate following the Vasicek [1977] dynamics. We find a closed-form solution for both the optimal investment strategy and the portfolio efficient frontier. We show that the mean-variance approach is equivalent to a “user-friendly” target-based approach optimisation problem which minimises a quadratic loss function. We show that the ruin probability can be kept under control through the choice of the target level. Numerical applications show that the proportions of bond and risky asset decrease when retirement approaches.