Competitive multi-player stochastic games with applications to multi-person financial contracts

Abstract

Competitive Multi-Player Stochastic Games with Applications to Multi-Person Financial Contracts Ivan Guo Abstract In the financial market, almost all traded derivatives only involve two parties. The aim of this thesis is to design and evaluate financial contracts involving multiple parties. This is done by utilising and extending concepts from game theory, financial mathematics and backward stochastic differential equations. The thesis is divided into two parts: multi-player stochastic competitive games and multi-person financial contracts. The first part of the thesis proposes two novel classes of multi-period multi-player stopping games: the multi-player redistribution game and the multi-player affine game. Both formulations are generalisations of the classic two-player Dynkin game, with a focus on designing the dependence between the payoffs of all players and their stopping decisions. These games are shown to be weakly unilaterally competitive, and sufficient conditions are given for the existence of optimal equilibria (a new solution concept motivated by financial applications), individual values and coalition values. The second part of the thesis introduces the notion of multi-person financial contracts by extending the two-person game option. These contracts may involve an arbitrary number of parties and each party is allowed to make a wide array of decisions, which then determines the settlement date as well as the payoffs. The generalised Snell envelope is introduced for the valuation of multi-person contracts and sufficient conditions for the existence of unique and additive arbitrage prices are provided. Finally, a new class of multi-dimensional reflected backward stochastic differential equations are proposed to model multi-person affine game options under market friction.