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Analysis of a drawdown-based regime-switching Lévy insurance model

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  • Landriault, David
  • Li, Bin
  • Li, Shu

Abstract

In this paper, we propose a new drawdown-based regime-switching (DBRS) Lévy insurance model in which the underlying drawdown process is used to model an insurer’s level of financial distress over time, and to trigger regime-switching transitions. By some analytical arguments, we derive explicit formulas for a generalized two-sided exit problem. We specifically state conditions under which the survival probability is not trivially zero (which corresponds to the positive security loading conditions of the proposed model). The regime-dependent occupation time until ruin is later studied. As a special case of the general DBRS model, a regime-switching premium model is given further consideration. Connections with other existing risk models (such as the loss-carry-forward tax model of Albrecher and Hipp, 2007) are established.

Suggested Citation

  • Landriault, David & Li, Bin & Li, Shu, 2015. "Analysis of a drawdown-based regime-switching Lévy insurance model," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 98-107.
  • Handle: RePEc:eee:insuma:v:60:y:2015:i:c:p:98-107
    DOI: 10.1016/j.insmatheco.2014.11.005
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    References listed on IDEAS

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    1. Vladimir Cherny & Jan Obłój, 2013. "Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model," Finance and Stochastics, Springer, vol. 17(4), pages 771-800, October.
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    8. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
    9. Vladimir Cherny & Jan Obloj, 2011. "Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model," Papers 1110.6289, arXiv.org, revised Apr 2013.
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    11. Albrecher, Hansjörg & Borst, Sem & Boxma, Onno & Resing, Jacques, 2009. "The tax identity in risk theory -- a simple proof and an extension," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 304-306, April.
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    1. repec:eee:insuma:v:79:y:2018:i:c:p:137-147 is not listed on IDEAS
    2. repec:eee:insuma:v:80:y:2018:i:c:p:45-53 is not listed on IDEAS
    3. repec:eee:stapro:v:129:y:2017:i:c:p:236-240 is not listed on IDEAS

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