Financial and Actuarial Mathematics: Time Table -------------------------------------------------------------------------- PV Schachermayer (Tuesday 16:30-18:00)

10.07.2001 - Michael Kirch (Humboldt Universität zu Berlin)

Title: Efficient Hedging under Model-Uncertainty

Abstract: We consider an investor who has sold an option and who now seeks to hedge against the induced risk using a fixed amount of capital. Efficient hedging strategies minimize the shortfall risk. If risk is measured by the expectation of the weighted shortfall, the remaining risk and the efficient hedging strategy depend on the "objective" probability measure (i.e. model) under consideration. However, the investor is typically faced with uncertainty about the appropriate model. We therefore allow for a class of different models and examine hedging strategies that are "robust" in the sense that they minimize the maximal shortfall risk. Here the maximum is taken over all models within the class. The solution to the corresponding mini-max problem is a saddle point. Under appropriate conditions, the robust-efficient strategy under model-uncertainty coincides with the efficient strategy for a fixed "worst-case" model. We also consider a stationary testing problem associated to the dynamic problem of efficient hedging. The maximin-optimal test for this problem can be described in terms of a worst-case pricing rule and a worst-case model, i.e., a "least-favorable pair".

Location: TU FH, Turm A, 6. Stock, Seminarraum 107 -------------------------------------------------------------------------- Web page: http://www.fam.tuwien.ac.at/schedule/ See also: http://www.fam.tuwien.ac.at/~vit/conf.html