On contingent claims pricing in incomplete markets: A risk sharing approach

TL;DR

This paper introduces a new risk sharing price for non-replicable claims in incomplete markets, based on utility maximization and convex combinations of utility differences, with proofs of existence and properties.

Contribution

It proposes the risk sharing price concept, providing existence proofs and property analysis, especially for exponential utility agents, advancing incomplete market pricing theory.

Findings

Existence of the risk sharing price for various utility functions

Properties of the risk sharing price established

Explicit analysis for exponential utility agents

Abstract

In an incomplete market setting, we consider two financial agents, who wish to price and trade a non-replicable contingent claim. Assuming that the agents are utility maximizers, we propose a transaction price which is a result of the minimization of a convex combination of their utility differences. We call this price the risk sharing price, we prove its existence for a large family of utility functions and we state some of its properties. As an example, we analyze extensively the case where both agents report exponential utility.