A General Model for Continuous Time Principal-Agent Problem Under Hidden Action

2026-07-19

AI Summary

This study addresses a continuous-time principal–agent problem in which the agent simultaneously chooses a hidden action and a consumption path, and the contract comprises both continuous payments and a lump-sum payment. The authors develop a general framework that models continuous compensation as a controlled diffusion process and directly links it to pay–performance sensitivity (PPS) measures commonly used in empirical literature. They introduce a novel set of sufficient conditions under which the agent’s problem can be solved explicitly without resorting to the first-order approach or subsequent verification steps. Drawing on stochastic control and continuous-time optimization theory, the paper derives analytically tractable example models that demonstrate the effectiveness and applicability of the proposed methodology.

Abstract

In this paper, we study a general continuous-time Principal-Agent (PA) problem, where the agent privately makes effort and consumption decisions over time under a contract with payment schemes both in continuous time and in lump sums. In particular, we allow the continuous payment process to be a controlled diffusion, which is directly related to the pay-to-performance sensitivity (PPS) in the empirical literature. In solving the agent's problem, we propose a new sufficient condition that directly yields a solution to the agent's problem, without requiring a separate verification step for the solution obtained from the first-order approach. We also present an example which can be solved explicitly.

Problem

• Principal-Agent problem
• continuous time
• hidden action
• pay-to-performance sensitivity
• contract theory

Innovation

• Principal-Agent problem
• continuous-time
• controlled diffusion
• pay-to-performance sensitivity
• first-order approach