Mathematical Aspects of Arbitrage | Department of Mathematics

Mathematical Aspects of Arbitrage

Event Information
Event Location: 
GAB 461, 4-5 PM; Refreshments: GAB 472, 3:30 PM
Event Date: 
Monday, November 3, 2014 - 4:00pm

Abstract:

We introduce models for financial markets and, in their context, the notions of "portfolio rules" and of "arbitrage". The normative assumption of "absence of arbitrage" is central in the modern theories of mathematical economics and finance. We relate it to probabilistic concepts such as "fair game", "martingale", "coherence" in the sense of deFinetti, and "equivalent martingale measure".

We also survey recent work in the context of the Stochastic Portfolio Theory pioneered by E.R. Fernholz. This theory provides descriptive conditions under which arbitrage, or "outperformance", opportunities do exist, then constructs simple portfolios that implement them. Finally we explain how, even in the presence of such arbitrage, most of the standard mathematical theory of finance still functions, though in somewhat modified form.