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Sample quantiles of heavy tailed stochastic processes

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  • Embrechts, Paul
  • Samorodnitsky, Gennady

Abstract

Distributions of sample quantiles of measurable stochastic processes are important for the purpose of rational pricing of "look-back" options. In this paper we compute the exact tail behavior of the sample quantile distribution for a large class of infinitely divisible stochastic processes with heavy tails.

Suggested Citation

  • Embrechts, Paul & Samorodnitsky, Gennady, 1995. "Sample quantiles of heavy tailed stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 217-233, October.
    • Handle: RePEc:eee:spapps:v:59:y:1995:i:2:p:217-233
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    References listed on IDEAS

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    1. Braverman, Michael & Samorodnitsky, Gennady, 1995. "Functionals of infinitely divisible stochastic processes with exponential tails," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 207-231, April.
    2. Miura, Ryozo, 1992. "A Note on Look-Back Options Based on Order Statistics," Hitotsubashi Journal of commerce and management, Hitotsubashi University, vol. 27(1), pages 15-28, November.
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    Cited by:

    1. Marcel Brautigam & Michel Dacorogna & Marie Kratz, 2019. "Pro-Cyclicality of Traditional Risk Measurements: Quantifying and Highlighting Factors at its Source," Papers 1903.03969, arXiv.org, revised Dec 2019.
    2. Rosnan Chotard & Michel Dacorogna & Marie Kratz, 2016. "Risk Measure Estimates in Quiet and Turbulent Times:An Empirical Study," Working Papers hal-01424285, HAL.
    3. Christian Genest & Johanna G. Nešlehová, 2020. "A Conversation With Paul Embrechts," International Statistical Review, International Statistical Institute, vol. 88(3), pages 521-547, December.
    4. Marcel, Bräutigam & Michel, Dacorogna & Marie, Kratz, 2018. "Predicting risk with risk measures : an empirical study," ESSEC Working Papers WP1803, ESSEC Research Center, ESSEC Business School.
    5. Braverman, Michael & Samorodnitsky, Gennady, 1998. "Distribution tails of sample quantiles and subexponentiality," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 45-60, August.
    6. Marcel Bräutigam & Michel Dacorogna & Marie Kratz, 2023. "Pro‐cyclicality beyond business cycle," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 308-341, April.

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