Hostname: page-component-669899f699-cf6xr Total loading time: 0 Render date: 2025-04-27T13:01:59.155Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Probabilistic methods, simulation and stochastic differential equations Stochastic processes

Published online by Cambridge University Press:  08 September 2016

Michael Schröder
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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).

Keywords

Laguerre series methods for stochastic functionalsladder height density

MSC classification

Primary: 65C50: Other computational problems in probability 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 60G99: None of the above, but in this section
Secondary: 33C90: Applications
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 38 , Issue 4 , December 2006 , pp. 969 - 994
Copyright
Copyright © Applied Probability Trust 2006 

References

Anh, V. V. and Leonenko, N. N. (1999). Non-Gaussian scenarios for the heat equation with singular initial conditions. Stoch. Process. Appl. 84, 91–114.Google Scholar
Apostol, T. (1974). Mathematical Analysis, 2nd edn. Addison-Wesley, Reading, MA.Google Scholar
Dufresne, D. (2000). Laguerre series for Asian and other options. Math. Finance 10, 407–428.Google Scholar
Dunford, N. and Schwartz, J. T. (1957). Linear Operators. Part I. John Wiley, New York.Google Scholar
Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G. (1953). Higher Transcendental Functions, Vol. 2. McGraw-Hill, New York.Google Scholar
Katznelson, Y. (1976). An Introduction to Harmonic Analysis, 2nd edn. Dover, New York.Google Scholar
Lebedev, N. N. (1972). Special Functions and Their Applications. Dover, New York.Google Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P. (1992). Numerical Recipes in C, 2nd edn. Cambridge University Press.Google Scholar
Sansone, G. (1991). Orthogonal Functions. Dover, New York.Google Scholar
Schröder, M. (2005). Laguerre series in contingent claim valuation, with applications to Asian options. Math. Finance 15, 491–531.Google Scholar
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, 995–1027.Google Scholar
Thangavelu, S. (1993). Lectures on Hermite and Laguerre Expansions. Princeton University Press.Google Scholar