Optimal strategy for a fund manager with option compensation

Abstract

I consider the problem of portfolio optimization for a manager whose compensation is given by the sum of a constant and a variable term. The constant term is a fixed percentage of the managed funds that is payed to the manager independently of his performance. The variable term is a premium that is proportional to the profit earned by the manager over a benchmark at a certain evaluation date. I find the optimal strategy and the optimal portfolio value in the Black–Scholes setting when the benchmark is a linear combination of the risky asset and the money market account.