Principal-agent problems with adverse selection: A stochastic target problem formulation

TL;DR

This paper reformulates a principal-agent problem with adverse selection as a stochastic target problem, enabling the analysis of contract design under information asymmetry and state constraints.

Contribution

It introduces a novel stochastic target problem formulation for principal-agent issues with adverse selection, extending the analysis beyond standard screening models.

Findings

Characterization of the credible domain for the stochastic target problem

Principal's problem reduced to a stochastic optimal control problem with partial information

Derivation of the value of screening contracts under the new framework

Abstract

We study a principal-agent problem with adverse selection, where the principal does not know the agent's true cost but must design a contract to optimize a specific criterion. Unlike standard screening frameworks that allow for self-selection, we assume the principal can only offer a unique contract. We show that the agent's optimization problem can be reformulated as a stochastic target problem. After characterizing the credible domain of this target problem, we show that the principal's objective can be solved as a stochastic optimal control problem with partial information and state constraints. The description of the credible domain also allows us to obtain the value of screening contracts.