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Revisiting integral functionals of geometric Brownian motion

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  • Boguslavskaya, Elena
  • Vostrikova, Lioudmila

Abstract

In this paper we revisit the integral functional of geometric Brownian motion It=∫0te−(μs+σWs)ds, where μ∈R, σ>0 and (Ws)s>0 is a standard Brownian motion.

Suggested Citation

  • Boguslavskaya, Elena & Vostrikova, Lioudmila, 2020. "Revisiting integral functionals of geometric Brownian motion," Statistics & Probability Letters, Elsevier, vol. 165(C).
    • Handle: RePEc:eee:stapro:v:165:y:2020:i:c:s0167715220301371
    DOI: 10.1016/j.spl.2020.108834
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    References listed on IDEAS

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    1. Daniel Dufresne, 2000. "Laguerre Series for Asian and Other Options," Mathematical Finance, Wiley Blackwell, vol. 10(4), pages 407-428, October.
    2. 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.
    3. De Schepper, A. & Goovaerts, M. & Delbaen, F., 1992. "The Laplace transform of annuities certain with exponential time distribution," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 291-294, December.
    4. P. Salminen & L. Vostrikova, 2016. "On exponential functionals of processes with independent increments," Papers 1610.08732, arXiv.org, revised Mar 2018.
    5. 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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