# Mathematisches Kolloquium

Am Donnerstag, 11.Juni 2015, um 16:30 Uhr spricht

## Marco Frittelli (Universität Mailand)

im HS A027 über das Thema

## Model-free Arbitrage and Super-hedging

Zusammenfassung: Mathematical models of finance are developed in order to answer two key questions: Pricing: What is a fair price for a traded security according to well established economical principles? Hedging: Every trade is connected to some risks arising from unfavorable future events. How does an agent cover such possible risks? These two questions represent the quintessence of Mathematical Finance and the answers are contained in the Fundamental Theorem of Asset Pricing (the equivalence between No Arbitrage and the existence of equivalent martingale measures) and the Super-hedging Duality Theorem (which relates the supremum of the prices of a claim g, under all equivalent martingale measures, to the cheapest portfolio that gives a payoff at least as good as g). So far however, the analysis has been developed under one crucial model assumption: the choice of a reference probability measure or, more recently, the choice of a family of such reference priors. Our aim instead is to investigate arbitrage and super-hedging conditions that are described independently of any reference probability or set of priors. In a discrete time financial market, we discuss different notions of Arbitrage, generated by a class S of significant sets, which we call Arbitrage de la classe S. The choice of S reflects into the intrinsic properties of the class of polar sets of martingale measures. From this we deduce several FTAP. In particular: for S={?}, absence of Model Independent Arbitrage is equivalent to the existence of a martingale measure; For S being the open sets, absence of Open Arbitrage is equivalent to the existence of full support martingale measures. We also provide a version of the Super-hedging Duality Theorem in terms of martingale measures with finite support. This talk is based on two papers joint with Matteo Burzoni and Marco Maggis
Alle Interessierten sind hiermit herzlich eingeladen. Eine halbe Stunde vor dem Vortrag gibt es Kaffee und Tee im Sozialraum (Raum 448) im 4. Stock.
Treffpunkt zum Abendessen um 18.00 Uhr wird noch bekannt gegeben.