Agents' agreement and partial equilibrium pricing in incomplete markets
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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 the 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 give a full characterization in this case. We, then, study a partial-equilibrium problem for a bundle of divisible claims and establish its existence and uniqueness. A number of technical results on conditional indifference prices are provided. Finally, we generalize the notion of partial-equilibrium pricing in the case where the agents' risk preferences are modelled by convex capital requirements.