Finance and Stochastics

, Volume 21, Issue 1, pp 111–155 | Cite as

Arbitrage-free pricing of multi-person game claims in discrete time

Article

Abstract

We introduce a class of financial contracts involving several parties by extending the notion of a two-person game option to a contract in which an arbitrary number of parties is involved and each of them is allowed to make a wide array of decisions at any time, not restricted to simply exercising the option. The collection of decisions by all parties then determines the contract’s termination date as well as the terminal payoff for each party. We provide sufficient conditions under which a discrete-time multi-person game option has a unique arbitrage-free price, which is additive with respect to any partition of the contract. Our results are illustrated by the detailed study of a particular multi-person contract with puttable tranches.

Keywords

Multi-person games Arbitrage-free pricing Optimal equilibrium 

Mathematics Subject Classification (2010)

60G35 91G20 91G80 

JEL Classification

G13 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Mathematical SciencesMonash UniversityMelbourneAustralia
  2. 2.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia
  3. 3.Faculty of Mathematics and Information ScienceWarsaw University of TechnologyWarsawPoland

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