Reward schemes

An investor has some funds invested through portfolio managers. By the end of the year, she reallocates the funds among these managers according to the managers' performance. While the investor tries to maximize her subjective utility (that depends on the total expected earnings), each portfolio manager tries to maximize the overall amount of funds bestowed in his hands to manage. A reward scheme is a rule that determines how funds should be allocated among the managers based on their performance. A reward scheme is optimal if it induces the (self-interested) managers to act in accordance with the interests of the investor. We show that an optimal reward scheme exists under quite general conditions.