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

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  • 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
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    References listed on IDEAS

    as
    1. Easley, David & Kiefer, Nicholas M, 1988. "Controlling a Stochastic Process with Unknown Parameters," Econometrica, Econometric Society, vol. 56(5), pages 1045-1064, September.
    2. N Baradel & B Bouchard & Ngoc Minh Dang, 2016. "Optimal trading with online parameters revisions," Papers 1604.06342, arXiv.org.
    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.
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    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.

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    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

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