Martedi 16 dicembre, alle ore 17, nella Sala dei Seminari del Dipartimento di Matematica dell'Universita' di Pisa, il prof. PETER BANK (Technische Universitat Berlin) terra' il seguente seminario:

SUPERREPLICATION WHEN TRADING AT MARKET INDIFFERENCE PRICES

Abstract

We consider a large investor who seeks to superreplicate a given contingent claim. Trading is done dynamically at market indifference prices as introduced in earlier joint work with D. Kramkov. The nonlinearities of this model for an illiquid financial market turn out to make this fundamental problem surprisingly intricate as the usual tools from convex analysis to prove, e.g., existence cannot be applied. Moreover, it is possible (and economically nonetheless reasonable) that an asset can be replicated with two different initial levels of wealth without this creating arbitrage opportunities. We introduce a notion of efficient friction suitable for this price impact model and show how this ensures existence of optimal superrelicating portfolios under some assumptions on the market makers utility functions. We also establish efficient friction to hold when payoffs of traded assets are specified via Levy processes or certain affine processes, e.g., like in Barndorff-Nielsen-Shepard stochastic volatility models. This is joint work with Selim Gokay.