Dynamic programming approach to principal-agent problems

TL;DR

This paper introduces a systematic method for solving general principal-agent problems with lump-sum payments by reducing them to stochastic control problems using dynamic programming and backward stochastic differential equations.

Contribution

It develops a novel approach that simplifies principal-agent problems into stochastic control problems, leveraging backward stochastic differential equations for non-Markovian cases.

Findings

Reduction of principal-agent problems to stochastic control problems

Use of backward stochastic differential equations for non-Markovian control

Identification of optimal contracts within a dynamic programming framework

Abstract

We consider a general formulation of the Principal-Agent problem with a lump-sum payment on a finite horizon, providing a systematic method for solving such problems. Our approach is the following: we first find the contract that is optimal among those for which the agent's value process allows a dynamic programming representation, for which the agent's optimal effort is straightforward to find. We then show that the optimization over the restricted family of contracts represents no loss of generality. As a consequence, we have reduced this non-zero sum stochastic differential game to a stochastic control problem which may be addressed by the standard tools of control theory. Our proofs rely on the backward stochastic differential equations approach to non-Markovian stochastic control, and more specifically, on the recent extensions to the second order case.