Optial Contract For The Principal-agent Under Knightian Uncertainty

Principal-agent theory is one of the important contents of modern economic contract theory.In real life,asymmetric information between principal and agent under the influence of moral hazard and adverse selection.In pursuit of maximizing the expected profit of the agent and the possible in the design of the contract deliberately withholding information.The agent in order to guarantee their expected earnings can appear the phenomenon such as lazy leading to agent's less effort.Based on the difference of expectation function between principal and agent and the lag of information,the normal operation of principal-agent contract may be disturbed.This requires us to design the optimal contract model of principal agent under the effective incentive condition.So that our model can guarantee the maximization of principal's expected profit under the premise of achieving the agent's expected profit.On the other hand,with the advent of the era of big data,information of the complexity and the uncertainty of the model itself will also bring to the stable operation of principal-agent contract a lot of interference.In order to explore the complexity of the information and the uncertainty of the model itself influence on decision-making of both principal and agent,we choice under the background of Knightian uncertainty study the optimal contract of the entrusted agent problem.In this paper,the optimal contract of principal agent in continuous time is taken as a classical model,assuming that the agent is risk averse and fuzzy averse and the principal is risk neutral and fuzzy averages.The utility function of Knightian uncertainty of the expected profit of the principal and the expected return of the agent is constructed by using the nonlinear expectation theory.Then the Hamilton-Jacobi-bellman(HJB)equation for the maximum expected profit of the principle is derived by using the principle of optimality under sublinear expectation.Finally,this paper takes the continuous value of the agent as the state variable.Numerically simulating the optimal expected profit of the principal,the agent's effort and consumption level under different uncertainty degree of Knightian.This paper analyzes the simulation results by combining the data and figures obtained from the numerical simulation with the knowledge of behavioral economics.Secondly,this paper under the background of Knightian uncertainty introduces the contract model in which the agent has external selection and the agent has promotion opportunity,which obtaining the utility functions of the expected profit of the principal and the expected return of the agent under the condition of the agent having external selection and promotion opportunity respectively by using the nonlinear expectation theory.Then this paper takes the agent's continuous value as the state variable and combines the G-Brownian motion and the G-Ito formula to derive the HJB equation that the maximum expected return of the principal satisfies.Through numerical simulation analyzes the specific decisions of the principal and agent under three conditions:the agent has no external choice,the agent has external choice and the agent has promotion opportunity.At last,this paper summarizes and forecasts the whole paper and puts forward some shortcomings and improvement methods.