Risk Minimization and Optimal Derivative Design in a Principal Agent Game

TL;DR

This paper studies how a principal can design optimal derivatives to minimize her risk in a setting with adverse selection, where agents have private risk aversion levels, extending previous models with new risk transfer insights.

Contribution

It introduces a model for optimal derivative design under adverse selection with heterogeneous, privately known risk aversion, extending prior theoretical frameworks.

Findings

Existence of a solution to the risk minimization problem.

Illustration of risk transfer effects on principal's income.

Extension of earlier models to include private risk aversion.

Abstract

We consider the problem of Adverse Selection and optimal derivative design within a Principal-Agent framework. The principal's income is exposed to non-hedgeable risk factors arising, for instance, from weather or climate phenomena. She evaluates her risk using a coherent and law invariant risk measure and tries minimize her exposure by selling derivative securities on her income to individual agents. The agents have mean-variance preferences with heterogeneous risk aversion coefficients. An agent's degree of risk aversion is private information and hidden to the principal who only knows the overall distribution. We show that the principal's risk minimization problem has a solution and illustrate the effects of risk transfer on her income by means of two specific examples. Our model extends earlier work of Barrieu and El Karoui (2005) and Carlier, Ekeland and Touzi (2007).