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On ladder height densities and Laguerre series in the study of stochastic functionals. I. Basic methods and results

  • Michael Schröder

Abstract

In this paper we develop methods for reducing the study, the computation, and the construction of stochastic functionals to those of standard concepts such as the moments of the pertinent random variables. Principally, our methods are based on the notion of ladder height densities and their Laguerre expansions, and our results provide a unifying framework for the distinct approaches of Dufresne (2000) and Schröder (2005).

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Corresponding author

Postal address: Keplerstrasse 30, D-69469 Weinheim (Bergstrasse), Germany.

References

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Dufresne, D. (2000). Laguerre series for Asian and other options. Math. Finance 10, 407428.
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Katznelson, Y. (1976). An Introduction to Harmonic Analysis, 2nd edn. Dover, New York.
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Sansone, G. (1991). Orthogonal Functions. Dover, New York.
Schröder, M. (2005). Laguerre series in contingent claim valuation, with applications to Asian options. Math. Finance 15, 491531.
Schröder, M. (2006). On ladder height densities and Laguerre series in the study of stochastic functionals. II. Exponential functionals of Brownian motion and Asian option values. Adv. Appl. Prob. 38, 9951027.
Thangavelu, S. (1993). Lectures on Hermite and Laguerre Expansions. Princeton University Press.
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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