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Parisian quasi-stationary distributions for asymmetric Lévy processes

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  • Czarna, Irmina
  • Palmowski, Zbigniew

Abstract

In recent years there has been some focus on quasi-stationary behavior of an one-dimensional Lévy process X, where we ask for the law P(Xt∈dy|τ0−>t) for t→∞ and τ0−=inf{t≥0:Xt<0}. In this paper we address the same question for so-called Parisian ruin time τθ, that happens when process stays below zero longer than independent exponential random variable with intensity θ.

Suggested Citation

  • Czarna, Irmina & Palmowski, Zbigniew, 2017. "Parisian quasi-stationary distributions for asymmetric Lévy processes," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 75-84.
    • Handle: RePEc:eee:stapro:v:127:y:2017:i:c:p:75-84
    DOI: 10.1016/j.spl.2017.03.011
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    References listed on IDEAS

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    1. Haas, Bénédicte & Rivero, Víctor, 2012. "Quasi-stationary distributions and Yaglom limits of self-similar Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 122(12), pages 4054-4095.
    2. Dickson,David C. M., 2016. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9781107154605.
    3. Dassios, Angelos & Wu, Shanle, 2008. "Ruin probabilities of the Parisian type for small claims," LSE Research Online Documents on Economics 32037, London School of Economics and Political Science, LSE Library.
    4. Hansjörg Albrecher & Dominik Kortschak & Xiaowen Zhou, 2012. "Pricing of Parisian Options for a Jump-Diffusion Model with Two-Sided Jumps," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(2), pages 97-129, July.
    5. Angelos Dassios & Shanle Wu, 2010. "Perturbed Brownian motion and its application to Parisian option pricing," Finance and Stochastics, Springer, vol. 14(3), pages 473-494, September.
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