Journal Article

Contract pricing and utility sharing

Michail Anthropelos, Nikolaos E. Frangos, Stylianos Z. Xanthopoulos and Athanasios N. Yannacopoulos

in IMA Journal of Management Mathematics

Published on behalf of Institute of Mathematics and its Applications

Volume 25, issue 3, pages 329-352
Published in print July 2014 | ISSN: 1471-678X
Published online May 2013 | e-ISSN: 1471-6798 | DOI: https://dx.doi.org/10.1093/imaman/dpt011
Contract pricing and utility sharing

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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 non-arbitrage 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 resort to indifference pricing, we suggest and explore a plausible scenario that allows for a natural interpretation of the agreed transaction price of the contract as the outcome of a sharing rule that takes into account the relative bargaining power of the two agents, expressed as a convex optimization problem. This leads to uniquely defined transaction prices, depending on the choice of parameters such as the bargaining power of the agents. The existence and uniqueness of such solutions is proved for a large family of utility functions, and a number of properties are stated and discussed. As an example, we analyse extensively the case where both agents have exponential utility.

Keywords: incomplete markets; indifference price; utility sharing price; bargaining power

Journal Article.  0 words. 

Subjects: Mathematics

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