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Special Semester on Stochastics with Emphasis on Finance
Linz, September 2008 - December 2008
Presentation: Kolmogorov equations and applications to path dependent derivatives

Workshop: Computational Methods with Applications in Finance, Insurance and the Life Sciences AND Stochastic Methods in Partial Differential Equations and Applications of Deterministic and Stochastic PDEs

Time: Thu, November 20, 2008, 16:20-17:10

Speaker: Andrea Pascucci

Abstract

The talk presents a survey of the theory of partial differential equations of Kolmogorov type arising in physics and in mathematical finance. These evolutionary equations, which are generally non-uniformly parabolic, are naturally associated to stochastic models with memory. Financial derivatives with dependence on the past provide some typical examples: in particular, Asian options of European and American style and the modeling of stochastic volatility for the evaluation of derivative securities will be discussed.

Presentation slides (pdf, 398 KB)

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