The Research On Optimal Of Private Fund Based On Principal-Agent Theory

The relationship between fund managers and external investors in private funds is a typical information asymmetry principal-agent relationship.This paper derives the optimal contract by static single-phase and continuous-time models,compares the conclusions of the two models and analyzes the parameters of the optimal contract and the influence of the variables on the optimal contract.When the exogenous variables change,the external Investors can protect the interests of external investors by adjusting the scale of asset management and the proportion of assets in the optimal contract to reduce moral hazard.In the static single-period principal-agent model,the optimal contract is firstly derived from the more realistic investment scale diminishing returns.After the analytical solution of the optimal contract is obtained,the high-water level and management rate can be known by analyzing the solution of the optimal contract.The relationship with the optimal share ratio;secondly,the optimal contract is derived under the condition that the return on investment scale is unchanged,and the optimal contract in the two cases is compared,and the conclusions obtained in the case of the same return on investment scale are found.However,many conclusions are not valid under the diminishing return on investment scale.The relationship between each parameter and the optimal contract is more intuitively seen through MATLAB.Based on the same research background,the model is extended to continuous time to study the principal-agent relationship.In the continuous time model,the rate of return is subject to a stochastic differential equation of mean regression,which takes into account the level of effort of fund managers,diminishing returns on investment scale,Market risk and other factors are more realistic.Through the stochastic differential equation of the rate of return and the participation constraint,the explicit expression of the optimal division scale can be known.Through this expression,how to adjust the proportion of the optimal contract when the parameters in the model change.At the same time,the fund's utility function can be obtained by using the fund's past highest yield and current rate of return as state variables,and then the incentive compatibility condition and objective function can be derived.The objective function satisfies an HJB equation and optimizes the HJB equation.Incentive compatibility conditions can be used to analyze the nature of the optimal asset size.