On Devising Various Alarm Systems for Insurance Companies
AbstractOne 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 defined 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 define 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 fixed 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.
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Bibliographic InfoPaper provided by ESSEC Research Center, ESSEC Business School in its series ESSEC Working Papers with number DR 10008.
Length: 58 pages
Date of creation: Dec 2010
Date of revision:
alarm system; capital accumulation function; efficiency; quantitative risk management; risk process; ruin probability;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-02-19 (All new papers)
- NEP-CIS-2011-02-19 (Confederation of Independent States)
- NEP-IAS-2011-02-19 (Insurance Economics)
- NEP-ORE-2011-02-19 (Operations Research)
- NEP-RMG-2011-02-19 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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, vol. 34(2), pages 159-174, April.
- 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.
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