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On Distributions Of Exponential Functionals Of The Processes With Independent Increments

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  • Lioudmila Vostrikova

    (LAREMA - Laboratoire Angevin de Recherche en Mathématiques - UA - Université d'Angers - CNRS - Centre National de la Recherche Scientifique)

Abstract

The aim of this paper is to study the laws of the exponential functionals of the processes X with independent increments , namely I t = t 0 exp(−X s)ds, t ≥ 0, and also I ∞ = ∞ 0 exp(−X s)ds. Under suitable conditions we derive the integro-differential equations for the density of I t and I ∞. We give sufficient conditions for the existence of smooth density of the laws of these function-als. In the particular case of Levy processes these equations can be simplified and, in a number of cases, solved explicitly.

Suggested Citation

  • Lioudmila Vostrikova, 2020. "On Distributions Of Exponential Functionals Of The Processes With Independent Increments," Working Papers hal-01725776, HAL.
    • Handle: RePEc:hal:wpaper:hal-01725776
    Note: View the original document on HAL open archive server: https://hal.science/hal-01725776v2
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    References listed on IDEAS

    as
    1. Jostein Paulsen, 2008. "Ruin models with investment income," Papers 0806.4125, arXiv.org, revised Dec 2008.
    2. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    3. Gjessing, Håkon K. & Paulsen, Jostein, 1997. "Present value distributions with applications to ruin theory and stochastic equations," Stochastic Processes and their Applications, Elsevier, vol. 71(1), pages 123-144, October.
    4. P. Salminen & L. Vostrikova, 2016. "On exponential functionals of processes with independent increments," Papers 1610.08732, arXiv.org, revised Mar 2018.
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    Cited by:

    1. Salminen, Paavo & Vostrikova, Lioudmila, 2019. "On moments of integral exponential functionals of additive processes," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 139-146.

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