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.