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A DIRECT SOLUTION TO THE FOKKER–PLANCK EQUATION FOR EXPONENTIAL BROWNIAN FUNCTIONALS

CAROLINE PINTOUX

Laboratoire de Mathématiques, Université de Poitiers, Téléport 2 – BP 30179, 86962 Chasseneuil, France

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and

NICOLAS PRIVAULT

Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong

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https://doi.org/10.1142/S0219530510001655Cited by:12 (Source: Crossref)

Abstract

The solution of the Fokker–Planck equation for exponential Brownian functionals usually involves spectral expansions that are difficult to compute explicitly. In this paper, we propose a direct solution based on heat kernels and a new integral representation for the square modulus of the Gamma function. A financial application to bond pricing in the Dothan model is also presented.

Keywords:

AMSC: 60J65, 60H30, 81S40, 33C10, 35A20, 91B24

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