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On Devising Various Alarm Systems for Insurance Companies

Author

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  • Marie Kratz

    (MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5 - UPD5 - Université Paris Descartes - Paris 5 - INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques - CNRS - Centre National de la Recherche Scientifique, ESSEC Business School)

  • Shubhabrata Das

    (IIMB - Indian Institute of Management Bangalore)

Abstract

One possible way of risk management for an insurance company is to develop an early and appropriate alarm system before the possible ruin. The ruin is de ned through the status of the aggregate risk process, which in turn is determined by premium accumulation as well as claim settlement out-go for the insurance company. The main purpose of this work is to design an effective alarm system, i.e. to de ne alarm times and to recommend augmentation of capital of suitable magnitude at those points to prevent or reduce the chance of ruin. In the three different methods outlined in this work, the alarms are signaled on the basis of the past history of the risk process and/or properties of claim distribution. Depending on the method adopted, the alarm time can be a random one or a xed parameter of the claim distribution (and premium function). The focus of this work is on devising a sequence of alarms, which are indeed xed parameters based on characteristics of the risk process. To draw a fair measure of effectiveness of alarm system(s), comparison is drawn between a process equipped with an alarm system, with capital being added at the sound of every alarm, and the corresponding process without any alarm system but an equivalently higher initial capital. Detailed analytical results are obtained for general processes and this is backed up simulated performances when the loss severity has exponential, or Pareto or discrete logarithmic distribution. The formulation is eventually intended to be applied and extended for devising alarm system for reinsurance contracts.

Suggested Citation

  • Marie Kratz & Shubhabrata Das, 2010. "On Devising Various Alarm Systems for Insurance Companies," Post-Print hal-00572546, HAL.
    • Handle: RePEc:hal:journl:hal-00572546
    Note: View the original document on HAL open archive server: https://essec.hal.science/hal-00572546
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    References listed on IDEAS

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    1. A. Guillou & P. Naveau & J. Diebolt & P. Ribereau, 2009. "Return level bounds for discrete and continuous random variables," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 584-604, November.
    2. Jean-Luc Besson & Michel M Dacorogna & Paolo de Martin & Michael Kastenholz & Michael Moller, 2009. "How Much Capital Does a Reinsurance Need?," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 34(2), pages 159-174, April.
    3. Ignatov, Zvetan G. & Kaishev, Vladimir K. & Krachunov, Rossen S., 2001. "An improved finite-time ruin probability formula and its Mathematica implementation," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 375-386, December.
    4. Dickson,David C. M., 2005. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521846400.
    5. Kaishev, Vladimir K. & Dimitrova, Dimitrina S., 2006. "Excess of loss reinsurance under joint survival optimality," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 376-389, December.
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    Cited by:

    1. Das, S. & Kratz, M., 2012. "Alarm system for insurance companies: A strategy for capital allocation," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 53-65.
    2. Dimitrina S. Dimitrova & Vladimir K. Kaishev & Shouqi Zhao, 2015. "Modeling Finite‐Time Failure Probabilities in Risk Analysis Applications," Risk Analysis, John Wiley & Sons, vol. 35(10), pages 1919-1939, October.

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