Discussion Papers 2021

CIRJE-F-1182	"Principal-Agent Problems with Hidden Savings in Continuous Time"
Author Name	Nakajima, Tomoyuki
Date	December 2021
Full Paper	PDF file
Remarks	Revised in April 2023.

Abstract
In this paper, we consider a continuous-time principal-agent problem with hidden savings. The agent’s problem, which is non-Markovian, is formulated using the stochastic HJB equation. Without loss of generality, attention is restricted to those contracts for which the agent optimally chooses zero savings. Then, the principal’s problem can be expressed as maximizing her expected profit subject 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. It coincides with the formulation obtained under the first-order approach.
Keywords: moral hazard; hidden savings; continuous time; weak formulation; first-order approach; stochastic HJB equations

Abstract

In this paper, we consider a continuous-time principal-agent problem with hidden savings. The agent’s problem, which is non-Markovian, is formulated using the stochastic HJB equation. Without loss of generality, attention is restricted to those contracts for which the agent optimally chooses zero savings. Then, the principal’s problem can be expressed as maximizing her expected profit subject 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. It coincides with the formulation obtained under the first-order approach.

Keywords: moral hazard; hidden savings; continuous time; weak formulation; first-order approach; stochastic HJB equations