Optimal portfolio delegation when parties have different coefficients of risk aversion

We consider the problem of delegated portfolio management when the involved parties are risk-averse. The agent invests the principal's money in the financial market, and in return he receives a compensation which depends on the value that he generates over some period of time. We use a dual approach to explicitly solve the agent's problem analytically and subsequently we use this solution to solve the principal's problem numerically. The interaction between the principal's and the agent's risk aversion and the optimal compensation scheme is studied and, for example, in the case of the more risk averse agent according to common folklore the principal should optimally choose a fee schedule such that the agent's derived risk aversion decreases. We illustrate that this is not always the case.