Book contents
- Frontmatter
- Contents
- Preface to first edition
- Preface to second edition
- 1 Introduction and mathematical preliminaries
- 2 Elementary probability
- 3 Random variables and their distributions
- 4 Location and dispersion
- 5 Statistical distributions useful in general insurance work
- 6 Inferences from general insurance data
- 7 The risk premium
- 8 Experience rating
- 9 Simulation
- 10 Estimation of outstanding claim provisions
- 11 Elementary risk theory
- References
- Solutions to exercises
- Author index
- Subject index
7 - The risk premium
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface to first edition
- Preface to second edition
- 1 Introduction and mathematical preliminaries
- 2 Elementary probability
- 3 Random variables and their distributions
- 4 Location and dispersion
- 5 Statistical distributions useful in general insurance work
- 6 Inferences from general insurance data
- 7 The risk premium
- 8 Experience rating
- 9 Simulation
- 10 Estimation of outstanding claim provisions
- 11 Elementary risk theory
- References
- Solutions to exercises
- Author index
- Subject index
Summary
Summary In this chapter we define risk premium and show why the two main components, claim frequency rate and claim size need to be considered separately. Exposure and its measurement are discussed, and examples of the use of the ‘eighths method’ and census method are given. We also discuss the problem of estimating the claim size distribution and mean claim size, and the calculation of premiums for policies subject to excesses and excess of loss reinsurance.
Risk premium; claim frequency and claim size
The pure premium or risk premium is the premium that would exactly meet the expected cost of the risk covered, ignoring management expenses, commission, contingency loadings, etc. To compute it, we need to estimate the claim frequency rate q and the mean claim size m. The risk premium is then qm. This assumes that the occurrence of a claim and its size are independent.
It is important that the two components: claim frequency rate and claim size be considered separately. Only in exceptional circumstances can the use of ‘rate of payment of claims’ be considered satisfactory for the assessment of a risk premium. The reasons for this include the following.
- Type
- Chapter
- Information
- Introductory Statistics with Applications in General Insurance , pp. 122 - 150Publisher: Cambridge University PressPrint publication year: 1999