Delegated portfolio management under ambiguity aversion

We examine the problem of setting optimal incentives to a portfolio manager (to be employed by an investor through a contract) making an ambiguity-robust portfolio choice with respect to estimation errors in expected returns. We consider a one-period model with a set of risky assets (with multivariate normal returns) whose expected returns are estimated with uncertainty and a linear sharing rule between a risk-neutral investor and a risk averse portfolio manager. The manager accepts the contract if the compensation o↵ered is at least as large as a minimum compensation he determines from his minimum acceptable utility level. Adopting a worst-case max min approach we obtain in closed-form the optimal compensation in various cases where the investor and the manager, respectively adopt or relinquish an ambiguity averse attitude. We apply our result to compute the compensation fees for an investment strategy restricted by Socially Responsible rules.