Abstract:

Based on the B lack-Scholes op tion p ricing theory, the equivalent martingale measure is constructed to obtain the op timal strategy of an op timal 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 simp lified as an unconstrained op timal investment strategy and a hedge strategy based on the European put-op tion and the two-asset exchange option.

Key words: minimum return constraint, optimal investment strategy, equivalent maningale measure