Moral hazard under ambiguity

TL;DR

This paper extends the Holmström and Milgrom model by incorporating volatility uncertainty, analyzing how worst-case volatility affects optimal contracts and comparing these results to classical models.

Contribution

It introduces a framework with ambiguity about output volatility, deriving optimal contracts under worst-case scenarios for both Agent and Principal.

Findings

Optimal contracts are linear in output and quadratic variation.

Worst-case volatility impacts the structure of optimal contracts.

Comparison shows differences from classical models.

Abstract

In this paper, we extend the Holmstro\"om and Milgrom problem [47] by adding uncertainty about the volatility of the output for both the Agent and the Principal. We study more precisely the impact of the "Nature" playing against the Agent and the Principal by choosing the worst possible volatility of the output. We solve the first--best and the second--best problems associated with this framework and we show that optimal contracts are in a class of contracts similar to [14, 15], linear with respect to the output and its quadratic variation. We compare our results with the classical problem in [47].