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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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    Keywords

    Optimal reinsurance; Partial information; Hawkes processes; Cox processes with shot noise; BSDEs;
    All these keywords.

    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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