委托代理制度下企业和代理人的最优策略研究  

A Research on the Optimal Strategies of Enterprises and Agents Under Principal-agent System

作　　者：李亚男 Ya Nan LI(School of Finance,Capital University of Economics and Business,Beijing 100070,P.R.China)

机构地区：[1]首都经济贸易大学金融学院,北京100070

出　　处：《数学学报（中文版）》2022年第3期547-558,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11901404)。

摘　　要：本文研究了存在信息不对称和委托代理冲突时企业的最优投资时刻,工资策略和代理人的最优努力程度选取问题.已知企业拥有对某项目的投资选择权,由于专业技术的限制,股东将委托代理者经营此投资项目.投资后,该项目产生两部分价值,一部分可被股东获知且和投资时刻相关,另一部分只有代理人能观察到,且这部分价值的分布和代理人的努力程度相关.股东要选择最优的投资时刻和工资水平,在使代理人不谎报项目收益的情况下最大化企业的净折现收益(总折现收益一代理人的折现工资).代理人要选择最优的努力程度来最大化自己的净折现工资收入(折现工资一折现努力).因为一方的策略会影响另一方的策略选取,所以这其实是一个带限制条件的零和博弈问题.本文将分别给出第二部分收益服从离散型分布和连续型分布两种情形下双方的最优策略和值函数.This paper studies the optimal investment time of a company,the selection of wage strategy of the company and the agent’s optimal effort degree under information asymmetry and principal agent conflicts.A company has an option to invest in a project.Because of technical limitations,the shareholders entrust an agent to manage the project investment problem.The project generates two parts of value.One part can be informed by shareholders,and the other part is only observed by the agent and the distribution of which is related to the degree of efforts of the agent.The shareholders should choose the best time of investment and the salary level to maximize the expected value of the company under the condition that the agent does not lie about the income of the project.The agent should choose the best degree of effort to maximize his net discounted salary(discounted wage-discounted effort).Because one party’s strategy will affect the choice of the other’s strategy,it is actually a game with restricted conditions.In this paper,we will get the optimal strategies and value functions of both sides for different distributions of project value.

关 键 词：信息不对称 最优投资时刻 委托代理冲突 HJB方程 

分 类 号：O211.6[理学—概率论与数理统计]