This paper investigates the optimal portfolio selection and contribution rate of an aggregate defined benefit pension plan. The pension manager invests in a financial market consisting of one risk-free asset and \(n\) risky assets, where the risky assets are modeled by a multi-dimensional CEV process. The manager faces heterogeneous preferences regarding both financial risk and contribution risk. We assume a stochastic benefit process, which introduces additional drift and diffusion terms, making the fund surplus process non-self-financing. To address this, we transform the original problem into an equivalent one using a replication method. The manager’s optimization objective is to maximize the weighted difference between the mean-variance criterion of the terminal fund wealth and a convex function of the contribution rate. The optimization objective includes a variance operator and a non-exponential discount function, leading to time-inconsistency. To address this, we adopt a game-theoretic framework to derive the equilibrium investment-contribution strategy that ensures time-consistency. We derive and solve the associated extended Hamilton-Jacobi-Bellman (HJB) equation. The equilibrium contribution rate is determined by the manager’s tolerance for contribution risk, the risk-free interest rate, and the function capturing contribution risk. The equilibrium investment strategy is obtained under four special cases and comprises both a myopic demand and a hedging demand. Finally, numerical results are presented to illustrate the economic behavior of the pension manager.
