Hedging and Derivative Pricing in Incomplete Market Models

The pricing of derivatives and the general choice of reasonable trading strategies are fundamental questions in mathematical finance. In incomplete market models perfect hedging strategies do not exist and the pricing based only on arbitrage arguments is not possible. One has to fall back on additional assumptions, e.g. equilibrium-type arguments. We suggest an approach based on local maximization of expected utility. This is an intuitive concept in discrete-time which can be extended to a general semimartingale framework by an appropritate limiting procedure. We avoid the more common way to optimize terminal wealth, since we want to ensure numerical tractability even in complex models. In order to obtain derivative prices, we assume that all investors in the derivative market apply optimal strategies in the above sense. Mathematically, this is to say that optimal trading strategies in the market without derivatives are also optimal in the enlarged market including all contingent claims. Hedging strategies and derivative prices are computed for a number of discrete- and continuous-time settings. Mathematically, the approach is based on local semimartingale characteristics and martingale problems

Additional information: http://www.stochastik.uni-freiburg.de
contact person: Eberlein E
Phone: 0761/203-5660
Email: eberlein@stochastik.uni-freiburg.de

Start of project: 1994
End of project: 2006

Albert-Ludwigs-University Freiburg
Eberlein E
Abteilung für Mathematische Stochastik
Prof. Dr. Ernst Eberlein
Ernst-Zermelo-Straße 1
79104 Freiburg i. Br.
Germany

Phone: +49 (0)761 203 5664
Fax: +49 (0)761 203 5661
Email: sekretariat@stochastik.uni-freiburg.de
http://www.stochastik.uni-freiburg.de/eberlein
Actual Research Report

• DFG, DFG

Black-Scholes-Theorie, Diskretisierung, Numerische Verfahren

• Kallsen J.: Semimartingale Modelling in Finance. Dissertation Universität Freiburg, 1998.