IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v79y2018icp137-147.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668717301920
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2017.12.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, August.
    4. Wenyuan Wang & Zhimin Zhang, 2019. "Optimal loss-carry-forward taxation for L\'{e}vy risk processes stopped at general draw-down time," Papers 1904.08029, arXiv.org.
    5. Noba, Kei, 2021. "On the optimality of double barrier strategies for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 73-102.
    6. Egami, Masahiko & Leung, Tim & Yamazaki, Kazutoshi, 2013. "Default swap games driven by spectrally negative Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 347-384.
    7. Feng, Runhuan & Shimizu, Yasutaka, 2014. "Potential measures for spectrally negative Markov additive processes with applications in ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 11-26.
    8. Bayraktar, Erhan & Kyprianou, Andreas E. & Yamazaki, Kazutoshi, 2013. "On Optimal Dividends In The Dual Model," ASTIN Bulletin, Cambridge University Press, vol. 43(3), pages 359-372, September.
    9. Zhang, Gongqiu & Li, Lingfei, 2023. "A general method for analysis and valuation of drawdown risk," Journal of Economic Dynamics and Control, Elsevier, vol. 152(C).
    10. Jean-François Renaud, 2019. "De Finetti’s Control Problem with Parisian Ruin for Spectrally Negative Lévy Processes," Risks, MDPI, vol. 7(3), pages 1-11, July.
    11. Li, Shu & Zhou, Xiaowen, 2022. "The Parisian and ultimate drawdowns of Lévy insurance models," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 140-160.
    12. David Landriault & Bin Li & Hongzhong Zhang, 2017. "A Unified Approach for Drawdown (Drawup) of Time-Homogeneous Markov Processes," Papers 1702.07786, arXiv.org.
    13. Neofytos Rodosthenous & Hongzhong Zhang, 2020. "When to sell an asset amid anxiety about drawdowns," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1422-1460, October.
    14. Kolkovska, Ekaterina T. & Martín-González, Ehyter M., 2016. "Gerber–Shiu functionals for classical risk processes perturbed by an α-stable motion," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 22-28.
    15. Wang, Wenyuan & Chen, Ping & Li, Shuanming, 2020. "Generalized expected discounted penalty function at general drawdown for Lévy risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 12-25.
    16. Griffin, Philip S. & Maller, Ross A. & Schaik, Kees van, 2012. "Asymptotic distributions of the overshoot and undershoots for the Lévy insurance risk process in the Cramér and convolution equivalent cases," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 382-392.
    17. Ivanovs, Jevgenijs, 2013. "A note on killing with applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 29-34.
    18. Christian Paroissin & Landy Rabehasaina, 2015. "First and Last Passage Times of Spectrally Positive Lévy Processes with Application to Reliability," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 351-372, June.
    19. Eric C. K. Cheung & David Landriault, 2012. "On a Risk Model with Surplus-dependent Premium and Tax Rates," Methodology and Computing in Applied Probability, Springer, vol. 14(2), pages 233-251, June.
    20. Palmowski, Z. & Surya, B.A., 2020. "Optimal valuation of American callable credit default swaps under drawdown of Lévy insurance risk process," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 168-177.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:79:y:2018:i:c:p:137-147. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.