On Agents' Agreement and Partial-Equilibrium Pricing in Incomplete Markets

TL;DR

This paper analyzes how two risk-averse agents negotiate prices for illiquid claims in incomplete markets, providing conditions for successful trades, asymptotic characterizations, and a partial-equilibrium framework.

Contribution

It offers necessary and sufficient conditions for negotiation success and characterizes partial-equilibrium prices in incomplete markets with non-traded endowments.

Findings

Conditions for successful negotiation are established.

Asymptotic analysis for small claims is provided.

Existence and uniqueness of partial-equilibrium prices are proven.

Abstract

We consider two risk-averse financial agents who negotiate the price of an illiquid indivisible contingent claim in an incomplete semimartingale market environment. Under the assumption that the agents are exponential utility maximizers with non-traded random endowments, we provide necessary and sufficient conditions for negotiation to be successful, i.e., for the trade to occur. We also study the asymptotic case where the size of the claim is small compared to the random endowments and we give a full characterization in this case. Finally, we study a partial-equilibrium problem for a bundle of divisible claims and establish existence and uniqueness. A number of technical results on conditional indifference prices are provided.