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Bayesian optimal investment and reinsurance with dependent financial and insurance risks

Author

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  • Bäuerle Nicole

    (Department of Mathematics, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany)

  • Leimcke Gregor

    (Department of Mathematics, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany)

Abstract

Major events like the COVID-19 crisis have impact both on the financial market and on claim arrival intensities and claim sizes of insurers. Thus, when optimal investment and reinsurance strategies have to be determined, it is important to consider models which reflect this dependence. In this paper, we make a proposal on how to generate dependence between the financial market and claim sizes in times of crisis and determine via a stochastic control approach an optimal investment and reinsurance strategy which maximizes the expected exponential utility of terminal wealth. Moreover, we also allow that the claim size distribution may be learned in the model. We give comparisons and bounds on the optimal strategy using simple models. What turns out to be very surprising is that numerical results indicate that even a minimal dependence which is created in this model has a huge impact on the optimal investment strategy.

Suggested Citation

  • Bäuerle Nicole & Leimcke Gregor, 2022. "Bayesian optimal investment and reinsurance with dependent financial and insurance risks," Statistics & Risk Modeling, De Gruyter, vol. 39(1-2), pages 23-47, January.
    • Handle: RePEc:bpj:strimo:v:39:y:2022:i:1-2:p:23-47:n:2
    DOI: 10.1515/strm-2021-0029
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