Contract pricing and utility sharing

Abstract

In an incomplete market setting, we consider two financial agents who are willing to trade as counterparties a contract that represents a non-replicable indivisible contingent claim. Market incompleteness allows for an infinity of nonarbitrage prices at which the contract can be traded. Furthermore, indivisibility of the contract does not allow for equilibrium pricing. Assuming that the agents are utility maximizers who will resort into indifference pricing, we suggest a scenario that allows for the establishment of a natural one-to-one correspondence between the agreed transaction price of the contract and the relative bargaining power of the two agents. This amounts to the solution of an optimization problem, seeking to maximize a convex combination of the indirect utilities of the two agents, weighted by their relative bargaining power and under the constraint that the trade takes place. In particular, given the utility functions of the two agents and their relative bargaining power, we obtain an optimal unique price for the contract. Its existence is proved for a large family of utility functions, and a number of its properties are stated and discussed. As an example, we analyze extensively the case where both agents have exponential utility.