The Principle-Agent Conflict Problem in a Continuous-Time Delegated Asset Management Model

Yanan Li,Chuanzheng Li,Xiaofeng Zong

doi:10.1155/2021/3770868

Abstract

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 γ f and γ m , respectively. Suppose that the investor entrusts his money to the fund manager. The return of the investment is determined by the manager’s effort level and incentive strategy, but the benefit belongs to the investor. In order to encourage the manager to work hard, the investor will determine the manager’s salary according to the terminal income. 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. The uncertain form of the incentive strategy implies that the problem is different from the classical stochastic optimal control problem. 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. Then, we employ the dynamic programming principle to solve the problem.

Highlights

Since professional asset management institutions can make efficient investment decisions, save investors’ time and effort, and simplify the investment process, more and more investors entrust their money to fund managers, securities firms, and other asset management organizations
E whole asset management process involves two parties: the investor and the manager. e return of the investment is closely related to the manager’s effort level and investment strategy, but the interests belong to the investor
Ere are many papers committed to solving principalagent conflict problems

Summary

Introduction

Since professional asset management institutions can make efficient investment decisions, save investors’ time and effort, and simplify the investment process, more and more investors entrust their money to fund managers, securities firms, and other asset management organizations. There are many papers committed to solving principal-agent conflict problems in continuous-time models, the delegated asset management problems are usually investigated in discrete-time models for the sake of simplicity. Us, there are some contributions in this paper: Mathematical Problems in Engineering (i) is paper considers the delegated asset management problem in a continuous-time model (ii) Learning from [19], this paper gives explicit value functions and the optimal strategies of both sides by expressing the investor’s incentive strategy in terms of two auxiliary processes and turning the problem into a classical stochastic differential game problem (iii) In order to make the model more realistic, this paper brings in risk sensitivity coefficients to represent the subjects’ risk aversion attitudes is paper is organized as follows.

The Principal-Agent Conflict Model

The Manager’s Optimization Problem

The Investor’s Optimization Problem