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Expected utility of the drawdown-based regime-switching risk model with state-dependent termination

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

Abstract

In this paper, we model an entity’s surplus process X using the drawdown-based regime-switching (DBRS) dynamics proposed in Landriault et al. (2015a). We introduce the state-dependent termination time to the model, and provide rationale for its introduction in insurance contexts. By examining some related potential measures, we first derive an explicit expression for the expected terminal utility of the entity in the DBRS model with Brownian motion dynamics. The analysis is later generalized to time-homogeneous Markov framework, where the spectrally negative Lévy model is also discussed as a special example. Our results show that, even considering the impact of the termination risk, the DBRS strategy can still outperform its counterparts in either single regime strategy. This study shows that the DBRS model is not myopic, as it not only helps to recover from significant losses, but also may improve the insurer’s overall welfare.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:79:y:2018:i:c:p:137-147
    DOI: 10.1016/j.insmatheco.2017.12.008
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    References listed on IDEAS

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    1. Biffis, Enrico & Kyprianou, Andreas E., 2010. "A note on scale functions and the time value of ruin for Lévy insurance risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 85-91, February.
    2. Florin Avram & Zbigniew Palmowski & Martijn R. Pistorius, 2007. "On the optimal dividend problem for a spectrally negative L\'{e}vy process," Papers math/0702893, arXiv.org.
    3. David Landriault & Bin Li & Hongzhong Zhang, 2017. "A Unified Approach for Drawdown (Drawup) of Time-Homogeneous Markov Processes," Papers 1702.07786, arXiv.org.
    4. Bernard, Carole & Hardy, Mary & Mackay, Anne, 2014. "State-Dependent Fees For Variable Annuity Guarantees," ASTIN Bulletin, Cambridge University Press, vol. 44(3), pages 559-585, September.
    5. 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.
    6. Dickson,David C. M., 2010. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521176750.
    7. Schuhmacher, Frank & Eling, Martin, 2011. "Sufficient conditions for expected utility to imply drawdown-based performance rankings," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2311-2318, September.
    8. Zhang, Hongzhong & Leung, Tim & Hadjiliadis, Olympia, 2013. "Stochastic modeling and fair valuation of drawdown insurance," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 840-850.
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    Cited by:

    1. 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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