Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On three methods for analytic Laplace inversion in the framework of Brownian motion and their excursions


Author: Michael Schröder
Journal: Quart. Appl. Math. 71 (2013), 549-572
MSC (2010): Primary 44A10, 41Axx, 33C15; Secondary 60J65, 91G20
DOI: https://doi.org/10.1090/S0033-569X-2013-01324-5
Published electronically: May 20, 2013
MathSciNet review: 3112828
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Abstract: Working in a framework originating with Brownian motion and its excursions, this paper establishes a two-step Laplace inversion method for determining a function which is known through its transform after a convolution with another function with a known transform. The first step here has as its domain the class of parabolic cylinder functions, and it develops analytic Laplace inversion of their reciprocals. The second step pertains to convolutions on the positive reals with analytic factors where one of them is of exponential-order decay to zero at the origin; it develops two Laplace-inversion-based methods for handling these by asymptotic expansions. The results are shown to have applications to finance, yielding series representations and asymptotic expansions for the valuation and hedging of Parisian barrier options.


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Additional Information

Michael Schröder
Affiliation: Keplerstraße 30, D-69469 Weinheim (Bergstraße), Germany

DOI: https://doi.org/10.1090/S0033-569X-2013-01324-5
Keywords: Brownian motion subject to excursion conditions, constructive methods for handling convolutions, analytic Laplace inversion, Parisian barrier options
Received by editor(s): October 4, 2011
Published electronically: May 20, 2013
Article copyright: © Copyright 2013 Brown University
The copyright for this article reverts to public domain 28 years after publication.


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