IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v117y2024icp16-44.html
   My bibliography  Save this article

Optimal control under uncertainty: Application to the issue of CAT bonds

Author

Listed:
  • Baradel, Nicolas

Abstract

We propose a general framework for studying optimal issue of CAT bonds in the presence of uncertainty on the parameters. In particular, the intensity of arrival of natural disasters is inhomogeneous and may depend on unknown parameters. Given a prior on the distribution of the unknown parameters, we explain how it should evolve according to the classical Bayes rule. Taking these progressive prior-adjustments into account, we characterize the optimal policy through a quasi-variational parabolic equation, which can be solved numerically. We provide examples of application in the context of hurricanes in Florida.

Suggested Citation

  • Baradel, Nicolas, 2024. "Optimal control under uncertainty: Application to the issue of CAT bonds," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 16-44.
    • Handle: RePEc:eee:insuma:v:117:y:2024:i:c:p:16-44
    DOI: 10.1016/j.insmatheco.2024.03.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668724000398
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2024.03.004?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. N Baradel & B Bouchard & Ngoc Minh Dang, 2016. "Optimal trading with online parameters revisions," Papers 1604.06342, arXiv.org.
    2. Easley, David & Kiefer, Nicholas M, 1988. "Controlling a Stochastic Process with Unknown Parameters," Econometrica, Econometric Society, vol. 56(5), pages 1045-1064, September.
    3. J. David Cummins, 2008. "CAT Bonds and Other Risk‐Linked Securities: State of the Market and Recent Developments," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 11(1), pages 23-47, March.
    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. David Landriault & Bin Li & Hong Li & Yuanyuan Zhang, 2024. "Contract Structure and Risk Aversion in Longevity Risk Transfers," Papers 2409.08914, arXiv.org.

    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. Wieland, Volker, 2000. "Monetary policy, parameter uncertainty and optimal learning," Journal of Monetary Economics, Elsevier, vol. 46(1), pages 199-228, August.
    2. Torsten Heinrich & Juan Sabuco & J. Doyne Farmer, 2022. "A simulation of the insurance industry: the problem of risk model homogeneity," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(2), pages 535-576, April.
    3. Tesfaselassie, M.F. & Schaling, E., 2010. "Managing disinflation under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2568-2577, December.
    4. Ali, S. Nageeb, 2018. "Herding with costly information," Journal of Economic Theory, Elsevier, vol. 175(C), pages 713-729.
    5. Vives, Xavier, 1997. "Learning from Others: A Welfare Analysis," Games and Economic Behavior, Elsevier, vol. 20(2), pages 177-200, August.
    6. Bergemann, Dirk & Valimaki, Juuso, 2002. "Entry and Vertical Differentiation," Journal of Economic Theory, Elsevier, vol. 106(1), pages 91-125, September.
    7. Barrieu, Pauline & Loubergé, Henri, 2013. "Reinsurance and securitisation of life insurance risk: The impact of regulatory constraints," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 135-144.
    8. Laura-Gabriela CONSTANTIN, 2014. "Catastrophe Bonds. From Structure to Strategy – A Cluster Analysis at European Level," Economia. Seria Management, Faculty of Management, Academy of Economic Studies, Bucharest, Romania, vol. 17(2), pages 304-317, December.
    9. International Monetary Fund, 2016. "Eastern Caribbean Currency Union: 2016 Discussion on Common Policies of Member Countries-Press Release and Staff Report," IMF Staff Country Reports 2016/333, International Monetary Fund.
    10. Beck, Gunter W. & Wieland, Volker, 2002. "Learning and control in a changing economic environment," Journal of Economic Dynamics and Control, Elsevier, vol. 26(9-10), pages 1359-1377, August.
    11. Wieland, Volker, 2000. "Learning by doing and the value of optimal experimentation," Journal of Economic Dynamics and Control, Elsevier, vol. 24(4), pages 501-534, April.
    12. Beker, Pablo F. & Espino, Emilio, 2011. "The dynamics of efficient asset trading with heterogeneous beliefs," Journal of Economic Theory, Elsevier, vol. 146(1), pages 189-229, January.
    13. Camargo, Braz, 2014. "Learning in society," Games and Economic Behavior, Elsevier, vol. 87(C), pages 381-396.
    14. Drobetz, Wolfgang & Schröder, Henning & Tegtmeier, Lars, 2020. "The role of catastrophe bonds in an international multi-asset portfolio: Diversifier, hedge, or safe haven?," Finance Research Letters, Elsevier, vol. 33(C).
    15. Alexander Braun, 2016. "Pricing in the Primary Market for Cat Bonds: New Empirical Evidence," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(4), pages 811-847, December.
    16. Massimo Mariani & Paola Amoruso & Raffaele Didonato & Alessandra Caragnano, 2018. "The Drivers of Cat Bond Spread in the Primary Market," International Journal of Business and Management, Canadian Center of Science and Education, vol. 13(2), pages 1-65, January.
    17. Wulan Anggraeni & Sudradjat Supian & Sukono & Nurfadhlina Binti Abdul Halim, 2022. "Earthquake Catastrophe Bond Pricing Using Extreme Value Theory: A Mini-Review Approach," Mathematics, MDPI, vol. 10(22), pages 1-22, November.
    18. J. Cummins & Georges Dionne & Robert Gagné & A. Nouira, 2009. "Efficiency of insurance firms with endogenous risk management and financial intermediation activities," Journal of Productivity Analysis, Springer, vol. 32(2), pages 145-159, October.
    19. Eckhard Platen & David Taylor, 2016. "Loading Pricing of Catastrophe Bonds and Other Long-Dated, Insurance-Type Contracts," Papers 1610.09875, arXiv.org.
    20. Nektarios Milton, 2011. "A Catastrophe Insurance System for the European Union," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 5(2), pages 1-22, July.

    More about this item

    Keywords

    Optimal control; Uncertainty; Bayesian filtering; Cat bonds; Hurricanes;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    Statistics

    Access and download statistics

    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:117:y:2024:i:c:p:16-44. 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.