最小收益约束下的最优投资问题

在最优投资问题的约束条件为收益不低于市场组合收益(随机收益)与固定保本收益最大者的情况下，采用Black-Scholes期权定价框架，构造等价鞅测度求解得到该优化问题的最优投资策略，同时在HARA效用函数下分析该投资问题的性质，发现在不同条件下，该投资策略可以退化为无约束最优投资策略、基于欧式看跌期权及两资产交换期权的套期保值策略．

Optimal Investment Problem Under Minimum Return Constraint

Based on the Black-Scholes option pricing theory, the equivalent martingale measure is constructed to obtain the optimal strategy of an optimal investment problem. This problem is under the constraint that the return is not less than the maximum of the market return (random return) and the constant guaranteed return. Meanwhile, by the analysis of the characteristics of this investment problem with HARA utility function, it is concluded that this investment strategy can be simplified as an unconstrained optimal investment strategy and a hedge strategy based on the European put-option and the two-asset exchange option.