Diving gains between a client and her agent (Q1424713)

The author describes the specific conditions of the contract between a client and her agent with limited liability. These conditions are characterized by the reasonable benchmark return rate \(r_0\) and the proportion \(\alpha\). The market is assumed to be complete and the agent aims to maximize the risk-neutral value of his profit subject to some expected shortfall constraint. Stochastic integration is used to describe outcomes of the investment strategy. The values of \(r_0\) and \(\alpha\) are found explicitly. Computations in a Black-Scholes model are presented.