Portfolio management with benchmark related incentives under mean reverting processes

We study the problem of a fund manager whose compensation depends on the relative performance with respect to a benchmark index. In particular, the fund manager’s risk-taking incentives are induced by an increasing and convex relationship of fund flows to relative performance. We consider a dynamically complete market with N risky assets and the money market account, where the dynamics of the risky assets exhibit mean reversions, either in the drift or in the volatility. The manager optimizes the expected utility of the final wealth, with an objective function that is non-concave. The optimal solution is found by using the martingale approach and a concavification method. The optimal wealth and the optimal strategy are determined by solving a system of Riccati equations. We provide a semi-closed solution based on the Fourier transform.