This paper investigates the optimal management of defined contribution pension plan under the Omega ratio and Value-at-Risk (VaR) constraint. Interest and inflation risks are considered, and the financial market consists of cash, a zero-coupon bond, an inflation-indexed zero-coupon bond, and a stock. The goal of the pension manager is to maximize the performance ratio of the real terminal wealth under the VaR constraint. An auxiliary process is introduced to transform the original problem into a self-financing problem. We obtain the optimal terminal wealth under different cases by combining the linearization method, the Lagrange dual method, the martingale method, and the concavification method. There are fourteen cases for the convex penalty function, and there are six cases for the concave penalty function. Besides, when the penalty and reward functions are both power functions, the explicit forms of the optimal investment strategies are obtained. Numerical examples are shown to illustrate the impacts of the performance ratio and VaR constraint.

本文研究了欧米茄比率和风险价值（VaR）约束下的定额供款养老金计划的优化管理。考虑了利息和通胀风险，金融市场由现金、零息债券、通胀指数零息债券和股票组成。养老金管理者的目标是在 VaR 约束下最大化实际终端财富的绩效比率。引入了一个辅助过程，将原始问题转化为自筹资金问题。我们将线性化方法、拉格朗日对偶方法、鞅方法和凹化方法相结合，得到了不同情况下的最优终端财富。凸惩罚函数有 14 种情况，凹惩罚函数有 6 种情况。除了，当惩罚函数和奖励函数都是幂函数时，得到最优投资策略的显式形式。数值例子用来说明性能比和风险价值约束的影响。