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

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

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

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

Specifying Reusable Components

Reusable software components need expressive specifications. This paper outlines a rigorous foundation to model-based contracts, a method to equip classes with strong contracts that support accurate design, implementation, and formal verification of reusable components. Model-based contracts conservatively extend the classic Design by Contract with a notion of model, which underpins the precise definitions of such concepts as abstract equivalence and specification completeness. Experiments applying model-based contracts to libraries of data structures suggest that the method enables accurate specification of practical software

Automated verification of model transformations based on visual contracts

The final publication is available at Springer via http://dx.doi.org/10.1007/s10515-012-0102-yModel-Driven Engineering promotes the use of models to conduct the different phases of the software development. In this way, models are transformed between different languages and notations until code is generated for the final application. Hence, the construction of correct Model-to-Model (M2M) transformations becomes a crucial aspect in this approach. Even though many languages and tools have been proposed to build and execute M2M transformations, there is scarce support to specify correctness requirements for such transformations in an implementation-independent way, i.e., irrespective of the actual transformation language used. In this paper we fill this gap by proposing a declarative language for the specification of visual contracts, enabling the verification of transformations defined with any transformation language. The verification is performed by compiling the contracts into QVT to detect disconformities of transformation results with respect to the contracts. As a proof of concept, we also report on a graphical modeling environment for the specification of contracts, and on its use for the verification of transformations in several case studies.This work has been funded by the Austrian Science Fund (FWF) under grant P21374-N13, the Spanish Ministry of Science under grants TIN2008-02081 and TIN2011-24139, and the R&D programme of the Madrid Region under project S2009/TIC-1650

Metamodel-based model conformance and multiview consistency checking

Model-driven development, using languages such as UML and BON, often makes use of multiple diagrams (e.g., class and sequence diagrams) when modeling systems. These diagrams, presenting different views of a system of interest, may be inconsistent. A metamodel provides a unifying framework in which to ensure and check consistency, while at the same time providing the means to distinguish between valid and invalid models, that is, conformance. Two formal specifications of the metamodel for an object-oriented modeling language are presented, and it is shown how to use these specifications for model conformance and multiview consistency checking. Comparisons are made in terms of completeness and the level of automation each provide for checking multiview consistency and model conformance. The lessons learned from applying formal techniques to the problems of metamodeling, model conformance, and multiview consistency checking are summarized