假设用相对业绩来评价资产管理人的业绩. 当其薪酬方案设 为相对业绩的凸型函数时,在存在投资策略和VaR风险约束下, 研究资产管理人 以最大化其所获的到期报酬的期望效用为目标的最优资产配置问题. 首先, 利用拉格朗日对偶理论求解了一个当拉格朗日乘子给定的情形下, 无约束的 效用最大化问题, 再找到使得无约束的优化问题等同于考虑VaR约束的优化问题的拉格 朗日乘子, 从而求得了最优相对业绩过程和最优追踪误差的解析解. 数值结果表明, 该凸型激励机制的薪酬计划会使得资产管理者增加风险承担, 然而, VaR约束能够对经 济状况不好时的风险管理起到一定的改进作用.

Assume that the performance of the asset manager is based on the relative performance. When the remuneration scheme is set to be a convex function of the relative performance, we investigate the asset allocation problem of an asset manager by maximizing the expected utility of the remuneration under portfolio and VaR constraints. We first apply the Lagrange duality theory to solve the VaR constraint-free maximization problem with fixed Lagrange multipliers and then find the correct Lagrange multipliers that makes the optimal solution of the unconstrained problem the same one for the VaR-constrained problem. The closed-form expressions for the optimal relative performance and tracking error are derived. Numerical results show that the convex scheme can induce the asset manager to take more risk. However, VaR constraint can improve the risk management for the bad economic states.