Optimal Contracts And Compensation Designs With Risk Management

To alleviate the problem of moral hazard caused by information asymmetry between the principal and agent,the principal needs to design a reasonable contract and the form of salary to motivate the agent to choose an appropriate strategy for consumption and effort.In this thesis,we study moral hazard models with single risk management and with multi-risk management in the framework of continuous-time principal-agent theory.We discuss the participants' optimal strategies when moral hazard exists and does not exist,and compare the obtained results,separately.We list the main contents of this thesis as follows.(1)We investigate the concrete forms of optimal contract and optimal form of wage in a generalized continuous time principal-agent model.In order to understand the impact of information asymmetry on participants' strategies,we study the optimal contracts in three information structures: full information,hidden action and hidden savings.Using the dynamic programming principle,we find the optimal form of wage including the basic wage and a commission measured by a pay-per-performance fraction of the output.Comparing the properties of the optimal contract in the three information structures,we find that,with the increase of the severity of information asymmetry,the principal should improve the pay-per-performance fraction to alleviate moral hazard.With the increase of risk,the pay-per-performance fraction will decrease when information asymmetry emerges,and gradually approaches that in the full information case.In order to attract agents to work in a complex environment,the principal needs to increase the base salary when the risk increases.In addition,only if the profit made by agent's ability is enough to cover the loss caused by the risk,the principal will hire the agent.(2)We study the optimal contract and salary in the structure of full information and hidden action in the continuous time principal-agent model with risk management.Since both the principal and agent are risk averse,the setting that agent can put effort to reduce risk is closer to the situation in real life.In this case,the agent can control the drift and volatility of output process through production management effort and risk management effort,respectively.Therefore,besides the base salary and commission,the optimal wage should include the factor relating to a penalty to risk.Our results show that the coefficients in the wage,including the pay-per-performance fraction and sensitivity to quadratic variation,do not rely on the risk of the project,while these coefficients under hidden action are highly risk-related and approach to those under full information as the risk increases.Comparing to the full information case,the agent under hidden action exerts less effort to improve the output of the project but pays more attention to manage the risk.In addition,the minimum requirement for the agent to get a job is higher in the case of hidden action.(3)We investigate the optimal contract and its properties in the principalagent model with multi-risk management.In order to analyze the influence caused by the risk to the principal,we study two different situations.One is partially hidden risk,the other is fully hidden risk.To prove that the wage obtained by dynamic programming approach is the optimal one,we use the method of stochastic maximization principle to obtain the optimal strategy and expected utility of the principal and agent.Comparing the optimal contracts in the two information structures,we find that the optimal production management effort of the agent and the expected utility of the principal will increase with the information that the principal can observe.Therefore,using her known information reasonably can benefit the principal's utility.(4)We discuss the optimal contracts and equilibrium asset prices in a delegated portfolio management problem under the framework of principal-agent theory.In this model,we assume that there is a financial market involving an investor(principal)and a fund manager(agent).The agent damages the principal's interests through a “shirking” action and hiding information about effort.We analyze optimal contracts and equilibrium asset prices in the cases that principal can and cannot observe the agent's effort,respectively.We show that when the manager's effort is observable,the optimal contract is related to the return of the market portfolio if the agency friction caused by the shirking action is serious,but is only related to the return of the manager's portfolio if shirking is not serious.The properties of market equilibrium indicate that the agent can improve his expected utility by hiding effort,but this action will cause loss to the principal's expected utility.When the principal's expected utility is too low,the agent will not be employed.Therefore,hidden effort will also bring certain unemployment risks to the agent.