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A spatial mixed Poisson framework for combination of excess-of-loss and proportional reinsurance contracts

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  • Cerqueti, Roy
  • Foschi, Rachele
  • Spizzichino, Fabio

Abstract

In this paper a purely theoretical reinsurance model is presented, where the reinsurance contract is assumed to be simultaneously of an excess-of-loss and of a proportional type. The stochastic structure of the set of pairs (claim's arrival time, claim's size) is described by a Spatial Mixed Poisson Process. By using an invariance property of the Spatial Mixed Poisson Processes, we estimate the amount that the ceding company obtains in a fixed time interval in force of the reinsurance contract.

Suggested Citation

  • Cerqueti, Roy & Foschi, Rachele & Spizzichino, Fabio, 2009. "A spatial mixed Poisson framework for combination of excess-of-loss and proportional reinsurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 59-64, August.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:1:p:59-64
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    References listed on IDEAS

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    1. Hurlimann, Werner, 1994. "A note on experience rating, reinsurance and premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 14(3), pages 197-204, July.
    2. Kaluszka, Marek, 2001. "Optimal reinsurance under mean-variance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 61-67, February.
    3. Dickson, David C. M. & Waters, Howard R., 1996. "Reinsurance and ruin," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 61-80, December.
    4. Dickson, David C.M. & Waters, Howard R., 1997. "Relative Reinsurance Retention Levels," ASTIN Bulletin, Cambridge University Press, vol. 27(2), pages 207-227, November.
    5. Hipp, Christian & Vogt, Michael, 2003. "Optimal Dynamic XL Reinsurance," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 193-207, November.
    6. Centeno, Maria de Lourdes, 2002. "Measuring the effects of reinsurance by the adjustment coefficient in the Sparre Anderson model," Insurance: Mathematics and Economics, Elsevier, vol. 30(1), pages 37-49, February.
    7. Suijs, Jeroen & De Waegenaere, Anja & Borm, Peter, 1998. "Stochastic cooperative games in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 209-228, July.
    8. Centeno, Maria de Lourdes, 1997. "Excess of Loss Reinsurance and the Probability of Ruin in Finite Horizon," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 59-70, May.
    9. Verlaak, Robert & Beirlant, Jan, 2003. "Optimal reinsurance programs: An optimal combination of several reinsurance protections on a heterogeneous insurance portfolio," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 381-403, October.
    10. Centeno, Lourdes, 1985. "On Combining Quota-Share and Excess of Loss," ASTIN Bulletin, Cambridge University Press, vol. 15(1), pages 49-63, April.
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    Cited by:

    1. Gu, Mengdi & Yang, Yipeng & Li, Shoude & Zhang, Jingyi, 2010. "Constant elasticity of variance model for proportional reinsurance and investment strategies," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 580-587, June.
    2. Roy Cerqueti & Marco Ventura, 2009. "A Discrete Model for Patent Valuation," ISAE Working Papers 120, ISTAT - Italian National Institute of Statistics - (Rome, ITALY).
    3. Cerqueti, Roy & Fenga, Livio & Ventura, Marco, 2018. "Does the U.S. exercise contagion on Italy? A theoretical model and empirical evidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 436-442.
    4. Cerqueti Roy & Ventura Marco, 2015. "Patent Valuation under Spatial Point Processes with Delayed and Decreasing Jump Intensity," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 15(2), pages 433-456, July.
    5. Gen Sakoda & Hideki Takayasu & Misako Takayasu, 2019. "Tracking Poisson Parameter for Non-Stationary Discontinuous Time Series with Taylor’s Abnormal Fluctuation Scaling," Stats, MDPI, vol. 2(1), pages 1-15, January.
    6. Foschi, Rachele, 2023. "A Point Processes approach to bicycle sharing systems’ design and management," Socio-Economic Planning Sciences, Elsevier, vol. 87(PB).

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