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Optimal reinsurance via BSDEs in a partially observable model with jump clusters

Author

Listed:
  • Matteo Brachetta

    (Politecnico di Milano)

  • Giorgia Callegaro

    (University of Padova)

  • Claudia Ceci

    (University of Rome La Sapienza)

  • Carlo Sgarra

    (Università di Bari)

Abstract

We investigate an optimal reinsurance problem when the loss process exhibits jump clustering features and the insurance company has restricted information about the loss process. We maximise expected exponential utility of terminal wealth and show that an optimal strategy exists. By exploiting both the Kushner–Stratonovich and Zakai approaches, we provide the equation governing the dynamics of the (infinite-dimensional) filter and characterise the solution of the stochastic optimisation problem in terms of a BSDE, for which we prove existence and uniqueness of a solution. After discussing the optimal strategy for a general reinsurance premium, we provide more explicit results in some relevant cases.

Suggested Citation

  • Matteo Brachetta & Giorgia Callegaro & Claudia Ceci & Carlo Sgarra, 2024. "Optimal reinsurance via BSDEs in a partially observable model with jump clusters," Finance and Stochastics, Springer, vol. 28(2), pages 453-495, April.
    • Handle: RePEc:spr:finsto:v:28:y:2024:i:2:d:10.1007_s00780-023-00523-z
    DOI: 10.1007/s00780-023-00523-z
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    References listed on IDEAS

    as
    1. Matteo Brachetta & Claudia Ceci, 2019. "A BSDE-based approach for the optimal reinsurance problem under partial information," Papers 1910.05999, arXiv.org, revised May 2020.
    2. Cao, Jingyi & Landriault, David & Li, Bin, 2020. "Optimal reinsurance-investment strategy for a dynamic contagion claim model," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 206-215.
    3. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2014. "A benchmark approach to risk-minimization under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 129-146.
    4. Hansjörg Albrecher & Søren Asmussen c, 2006. "Ruin probabilities and aggregrate claims distributions for shot noise Cox processes," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2006(2), pages 86-110.
    5. Irgens, Christian & Paulsen, Jostein, 2004. "Optimal control of risk exposure, reinsurance and investments for insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 21-51, August.
    6. Brachetta, M. & Ceci, C., 2020. "A BSDE-based approach for the optimal reinsurance problem under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 1-16.
    7. Liang, Zhibin & Bayraktar, Erhan, 2014. "Optimal reinsurance and investment with unobservable claim size and intensity," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 156-166.
    8. Brachetta, M. & Ceci, C., 2019. "Optimal proportional reinsurance and investment for stochastic factor models," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 15-33.
    9. Antonis Papapantoleon & Dylan Possamai & Alexandros Saplaouras, 2016. "Existence and uniqueness results for BSDEs with jumps: the whole nine yards," Papers 1607.04214, arXiv.org, revised Nov 2018.
    10. Michael Mania & Marina Santacroce, 2010. "Exponential utility maximization under partial information," Finance and Stochastics, Springer, vol. 14(3), pages 419-448, September.
    Full references (including those not matched with items on IDEAS)

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    Keywords

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    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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