Discussion Papers 2022

CIRJE-F-1183	"Principal-Agent Problems with Hidden Savings in Continuous Time: Validity of the First-Order Approach"
Author Name	Nakajima, Tomoyuki
Date	December 2021
Full Paper	PDF file
Remarks

Abstract
In this paper, I establish the validity of the first-order approach to the continuous- time principal-agent problem with hidden savings. The agent’s problem, which is non- Markovian, is formulated using a stochastic HJB equation. Without loss of generality, the payment process is designed so that it is optimal for the agent to choose zero savings. Then, the principal’s problem can be expressed as maximizing her expected profit sub- ject to two SDEs: one equation describing the agent’s continuation utility process, and the other being the Euler equation concerning the agent’s marginal utility process.
Keywords: moral hazard; hidden savings; continuous time; weak formulation; firstorder approach; stochastic HJB equations

Abstract

In this paper, I establish the validity of the first-order approach to the continuous- time principal-agent problem with hidden savings. The agent’s problem, which is non- Markovian, is formulated using a stochastic HJB equation. Without loss of generality, the payment process is designed so that it is optimal for the agent to choose zero savings. Then, the principal’s problem can be expressed as maximizing her expected profit sub- ject to two SDEs: one equation describing the agent’s continuation utility process, and the other being the Euler equation concerning the agent’s marginal utility process.

Keywords: moral hazard; hidden savings; continuous time; weak formulation; firstorder approach; stochastic HJB equations