Summary
It is shown that moments of negative order as well as positive non-integral order of a nonnegative random variable X can be expressed by the Laplace transform of X. Applying these results to certain first passage times gives explicit formulae for moments of suprema of Bessel processes as well as strictly stable Lévy processes having no positive jumps.
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© 2002 Springer-Verlag Berlin Heidelberg
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Schürger, K. (2002). Laplace Transforms and Suprema of Stochastic Processes. In: Sandmann, K., Schönbucher, P.J. (eds) Advances in Finance and Stochastics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04790-3_15
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DOI: https://doi.org/10.1007/978-3-662-04790-3_15
Publisher Name: Springer, Berlin, Heidelberg
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