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

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Anthropelos, Michail
Zitkovic, Gordan
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Abstract
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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.
Keywords
Quantitative Finance - Pricing of Securities, Mathematics - Optimization and Control, Mathematics - Probability, Quantitative Finance - Trading and Market Microstructure, 91B70
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