Seminar on September 25 - Abhishek Ranjan

Title:              Arbitrage Structure and Finite Date Model with Financial Restriction
Speaker:       Dr Abhishek Ranjan

Department of Applied Mathematics
Université Paris 1 Panthéon Sorbonne, France

Time:               2 pm, Wednesday, September 25, 2013.

Venue:             TBA

Abstract:         We consider a (T+1)-date model of a financial exchange economy with finitely many agents having non-ordered preferences and portfolio constraints. There is a market for physical commodities for every state today and in the future, and financial transfers across time and states are allowed by means of finitely many nominal or numeraire assets. We examine the properties of the financial structure F and the set of its (limited) arbitrage-free prices Q_F. The set of arbitrage-free prices is shown to be a convex cone under a sufficient condition that holds in particular for short lived assets. Furthermore, we provide examples of equivalent financial structures F and F’ such that Q_F is a convex cone, but Q_F’ is neither convex nor a cone. At the end, we provide several existence results of equilibrium in a financial exchange economy for which portfolios are either defined by linear constraints or a convex set extending the framework of unconstrained case by Cass (1984, 2006), Werner (1985), Duffie (1987), Gaenakopolos and Polemarchakis (1997), framework of linear equality constraints by Balasko et al. (1990) and framework of 2-date by Cornet and Gopalan (2007), Aouani and Cornet (2011, 2013).

About the Speaker:   Dr Ranjan completed his PhD from the Paris School of Economics and Université Paris 1 Panthéon Sorbonne in 2012. His research interests are in Applied Mathematics, General Equilibrium Models, Financial Economics, and Decision Under Uncertainty.