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Agent's Optimal Compensation Under Inflation Risk by Using Dynamic Contract Model.

Chen Fei1, Weiyin Fei2, Fanhong Zhang3

  • 1School of Business, University of Shanghai for Science and Technology, Shanghai, 200093 China.

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|January 17, 2022
PubMed
Summary
This summary is machine-generated.

This study analyzes principal-agent dynamics with hidden effort in continuous time, incorporating inflation. Inflation risk significantly impacts agent compensation based on the firm

Keywords:
Equity incentiveItô formulainflation riskprincipal-agent problemthe martingale representation theorem

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Area of Science:

  • Financial Economics
  • Contract Theory
  • Stochastic Calculus

Background:

  • Principal-agent problems with moral hazard are common in continuous-time financial settings.
  • Existing models often do not account for inflation's impact on firm cash flows and agent compensation.
  • Geometric Brownian Motion (GBM) is a standard model for firm cash flow dynamics.

Purpose of the Study:

  • To extend dynamic optimal contract theory to an inflation environment.
  • To analyze the effect of inflation risk on principal-agent compensation.
  • To investigate how a firm's market position influences compensation under inflation.

Main Methods:

  • Utilizing Itô's formula to derive the firm's real cash flow dynamics under inflation.
  • Applying the martingale representation theorem to determine the agent's continuation value process.
  • Solving the Hamilton-Jacobi-Bellman (HJB) equation to derive the investor's scaled value function via a second-order ordinary differential equation.

Main Results:

  • The study derives the dynamic equation for real cash flow in an inflationary environment.
  • The agent's continuation value process is determined using martingale theory.
  • Inflation risk's influence on optimal agent compensation is shown to be dependent on the firm's market standing.

Conclusions:

  • Inflation introduces complexities into principal-agent contracts, affecting optimal compensation structures.
  • The firm's market position is a critical factor in how inflation risk shapes agent incentives.
  • This research provides a framework for understanding dynamic contracts in inflationary economic conditions.