On Devising Various Alarm Systems for Insurance Companies

Marie Kratz () and Shubhabrata Das
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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

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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.

Keywords: alarm system; capital accumulation function; efficiency; quantitative risk management; risk process; ruin probability (search for similar items in EconPapers)
Date: 2010-12
Note: View the original document on HAL open archive server: https://essec.hal.science/hal-00572546
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Citations: View citations in EconPapers (2)

Published in 2010

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