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Indifference Pricing of Reinsurance with Reinstatements Using Coherent Monetary Criteria

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  • Nabil Kazi-Tani

    (LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

We consider the problem of indifference pricing of reinsurance contracts that contain a reinstatement clause. We define the indifference price relative to both a monetary utility function and a risk measure, to take into account both the risk reduction and the relief of capital immobilization provided by reinsurance. We characterize the indifference price as the unique solution to a fixed point equation and we bound the price by two easily computable values, if one has access to losses simulations. We illustrate our results on a European catastrophe insurance portfolio, and we conduct a simulation study for comparison and reproducibility purposes, where we include the case of dependence between claim arrivals, using Hawkes processes.

Suggested Citation

  • Nabil Kazi-Tani, 2021. "Indifference Pricing of Reinsurance with Reinstatements Using Coherent Monetary Criteria," Post-Print hal-01742638, HAL.
    • Handle: RePEc:hal:journl:hal-01742638
    DOI: 10.1007/s13385-020-00257-8
    Note: View the original document on HAL open archive server: https://hal.science/hal-01742638v2
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    References listed on IDEAS

    as
    1. Griselda Deelstra & Guillaume Plantin, 2014. "Risk Theory and Reinsurance," SciencePo Working papers Main hal-03256838, HAL.
    2. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    3. Hess, Klaus TH. & Schmidt, Klaus D., 2004. "Optimal Premium Plans for Reinsurance with Reinstatements," ASTIN Bulletin, Cambridge University Press, vol. 34(2), pages 299-313, November.
    4. E. Jouini & W. Schachermayer & N. Touzi, 2008. "Optimal Risk Sharing For Law Invariant Monetary Utility Functions," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 269-292, April.
    5. repec:dau:papers:123456789/361 is not listed on IDEAS
    6. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    7. repec:hal:spmain:info:hdl:2441/2iocb3a66198q8ovlu1gfkqie7 is not listed on IDEAS
    8. Griselda Deelstra & Guillaume Plantin, 2014. "Risk Theory and Reinsurance," Sciences Po publications info:hdl:2441/2iocb3a6619, Sciences Po.
    9. Griselda Deelstra & Guillaume Plantin, 2014. "Risk Theory and Reinsurance," SciencePo Working papers hal-03256838, HAL.
    10. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    11. Mata, Ana J., 2000. "Pricing Excess of Loss Reinsurance with Reinstatements," ASTIN Bulletin, Cambridge University Press, vol. 30(2), pages 349-368, November.
    12. Griselda Deelstra & Guillaume Plantin, 2014. "Risk Theory and Reinsurance," Post-Print hal-03256838, HAL.
    Full references (including those not matched with items on IDEAS)

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