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3 - Short term risk models

Published online by Cambridge University Press:  05 August 2012

Roger J. Gray
Affiliation:
Heriot-Watt University, Edinburgh
Susan M. Pitts
Affiliation:
University of Cambridge
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Summary

One of the key quantities of interest to an insurance company is the total amount to be paid out on a particular portfolio of policies over a fixed time interval, such as an accounting period. This quantity may be approached in various ways, and we mention two popular models below. We refer to both these models as examples of short term risk models because they model a risk over a fixed time period. This is in contrast to the classical risk model in Chapter 6, where the stochastic evolution of the flow of claim payments and premium income is modelled over time, and properties of this evolution over an infinite time period are derived. As might be expected, the techniques and results of Chapter 6 are deeper and more complex than those in this chapter, but they build on the foundations that we develop here for short term models.

One short term model is the individual risk model, where we consider the portfolio to consist of a fixed number, n, of independent policies, and the total amount claimed on the portfolio in a fixed time period is modelled as a random variable T, given by

T=Y1+ ... +Yn,

where Yi is the total amount claimed on policy i, and Y1, …, Yn are assumed to be independent, but not necessarily identically distributed. It turns out that it is more difficult than might be expected at first sight to deal with this apparently simple quantity in terms of numerical calculations and in terms of obtaining analytical expressions for the distribution of T. This model is considered in §3.8.

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Chapter
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Risk Modelling in General Insurance
From Principles to Practice
, pp. 90 - 146
Publisher: Cambridge University Press
Print publication year: 2012

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  • Short term risk models
  • Roger J. Gray, Heriot-Watt University, Edinburgh, Susan M. Pitts, University of Cambridge
  • Book: Risk Modelling in General Insurance
  • Online publication: 05 August 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139033756.004
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  • Short term risk models
  • Roger J. Gray, Heriot-Watt University, Edinburgh, Susan M. Pitts, University of Cambridge
  • Book: Risk Modelling in General Insurance
  • Online publication: 05 August 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139033756.004
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Short term risk models
  • Roger J. Gray, Heriot-Watt University, Edinburgh, Susan M. Pitts, University of Cambridge
  • Book: Risk Modelling in General Insurance
  • Online publication: 05 August 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139033756.004
Available formats
×