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The randomly stopped geometric Brownian motion

Author

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  • Balanzario, Eugenio P.
  • Ramírez, Rosalva Mendoza
  • Ortiz, Jorge Sánchez

Abstract

In this short note we compute the probability density function of the random variable XT, where Xt is a geometric Brownian motion, and where T is a random variable independent of Xt and has either a Gamma distribution or it is uniformly distributed. In the last section of the note, the distribution obtained for XT is fitted to the data consisting in the academic production of a set of mathematicians.

Suggested Citation

  • Balanzario, Eugenio P. & Ramírez, Rosalva Mendoza & Ortiz, Jorge Sánchez, 2014. "The randomly stopped geometric Brownian motion," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 85-92.
  • Handle: RePEc:eee:stapro:v:90:y:2014:i:c:p:85-92
    DOI: 10.1016/j.spl.2014.03.013
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
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    4. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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    Cited by:

    1. Johnston, Josh & Andersen, Tim, 2022. "Random processes with high variance produce scale free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).

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