[en] This project aims to study, with an axiomatic approach, financial systems in systemic risk under the principles of limited liability of equity, proportionality, and priority of debt claims. Following the steps in the article by Larry Eisenberg and Thomas H. Noe, Systemic Risk in Financial Systems, Management Science 47(2): 236-249, 2001, we prove results related to the existence, uniqueness, and characterisation of solutions. Finally, we apply to our framework the no advantageous merging and no advantageous splitting concepts outlined by M. Angeles de Frutos in Coalitional manipulations in a bankruptcy problem, Review of Economic Design 4, 255-272, 1999, in order to estudy their compatibility along the principles of limited liability of equity, proportionality, and priority of debt claims.

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Pere Calleja