In this paper, we first express the investor’s incentive strategy in term of two auxiliary processes and turn this problem into a classical one. The uncertain form of the incentive strategy implies that the problem is different from the classical stochastic optimal control problem. This is a stochastic differential game problem, and the distribution of income between the manager and the investor is a key point to be solved in the custody model. In order to encourage the manager to work hard, the investor will determine the manager’s salary according to the terminal income. The return of the investment is determined by the manager’s effort level and incentive strategy, but the benefit belongs to the investor. Suppose that the investor entrusts his money to the fund manager. This paper considers the principle-agent conflict problem in a continuous-time delegated asset management model when the investor and the fund manager are all risk-averse with risk sensitivity coefficients, respectively.
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