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Indifference Pricing of Reinsurance with Reinstatements Using Coherent Monetary Criteria

Author

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  • Nabil Kazi-Tani

    (SAF - 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, 2020. "Indifference Pricing of Reinsurance with Reinstatements Using Coherent Monetary Criteria," Working Papers hal-01742638, HAL.
    • Handle: RePEc:hal:wpaper:hal-01742638
    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. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    2. 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.
    3. 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.
    4. repec:dau:papers:123456789/361 is not listed on IDEAS
    5. Mata, Ana J., 2000. "Pricing Excess of Loss Reinsurance with Reinstatements," ASTIN Bulletin, Cambridge University Press, vol. 30(2), pages 349-368, November.
    6. Gerber, Hans U., 1974. "On Additive Premium Calculation Principles," ASTIN Bulletin, Cambridge University Press, vol. 7(3), pages 215-222, March.
    7. Panjer, Harry H., 1981. "Recursive Evaluation of a Family of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 22-26, June.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Insurance premium calculation; Convex risk measures; Concave monetary utility functions; Reinstatements; Reinsurance layers;
    All these keywords.

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