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B. Düring:
"An inverse problem in option pricing and kinetic models for wealth distribution";
Vortrag: FAM-Seminar, Wien (eingeladen); 11.12.2007.

s. engl. Abstract

Numerical Methods for optimal control of systems described by partial differential equations (PDE) have been studied widely and successfully applied to many problems. In the first part of this talk we consider the problem of identifying local volatility functions from market option prices. Mathematically the problem can be formulated as a PDE constrained optimal control problem. We propose an algorithm that is based on sequential quadratic programming and on a primal-dual active set strategy that guarantees pointwise bilateral constraints for the volatility. We present analytical and numerical results.

In the second part of the talk, we consider kinetic agent models for wealth distribution in simple economies. Based on `microscopic' interactions these models develop `macroscopic' features in the long-term limit like stationary wealth distributions with Pareto tails that are observed also in empirical data. We report some recent analytical and numerical results on the speed of relaxation towards the stationary state.

Inverse problem, option pricing, kinetic model, wealth distribution

Projektleitung Ansgar Jüngel:
Numerik und Modellierung nichtlinearer partieller Differentialgleichungen zur Beschreibung von Kredit- und Preisrisiken