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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.

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  • 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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    Cited by:

    1. Lesław Gajek & Marcin Rudź, 2020. "Finite-Horizon Ruin Probabilities in a Risk-Switching Sparre Andersen Model," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1493-1506, December.
    2. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, January.
    3. Landriault, David & Li, Bin & Li, Shu, 2018. "Expected utility of the drawdown-based regime-switching risk model with state-dependent termination," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 137-147.
    4. Ceren Vardar-Acar & Mine Çağlar & Florin Avram, 2021. "Maximum Drawdown and Drawdown Duration of Spectrally Negative Lévy Processes Decomposed at Extremes," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1486-1505, September.
    5. Gajek, Lesław & Rudź, Marcin, 2018. "Banach Contraction Principle and ruin probabilities in regime-switching models," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 45-53.
    6. Lesław Gajek & Marcin Rudź, 2020. "Finite-horizon general insolvency risk measures in a regime-switching Sparre Andersen model," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1507-1528, December.
    7. Jingchao Li & Bihao Su & Zhenghong Wei & Ciyu Nie, 2022. "A Multinomial Approximation Approach for the Finite Time Survival Probability Under the Markov-modulated Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2169-2194, September.
    8. Gajek, Lesław & Rudź, Marcin, 2017. "A generalization of Gerber’s inequality for ruin probabilities in risk-switching models," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 236-240.
    9. Landriault, David & Li, Bin & Wong, Jeff T.Y. & Xu, Di, 2018. "Poissonian potential measures for Lévy risk models," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 152-166.

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