Statistical motor rating: making effective use of your data

Abstract

The paper gives details of statistical modelling techniques which can be used to estimate risk and office premiums from past claims data. The methods described allow premiums to be estimated for any combinaton of rating factors, and produce standard errors of the risk premium. The statistical package GLIM is used for analysing claims experience, and GLIM terminology is used and explained thoughout the paper.Arguments are put forward for modelling frequency and severity separately for different claim types. Pitted values can be used to estimate risk premiums, and the incorporation of expenses allows for the estimation of office premiums. Particular attention is given to the treatment of no claim discount.The paper also discusses possible uses of the modelled premiums. These include the construction of 'standardised' one way tables and the analysis of experience by postal code and model of vehicle. Also discussed is the possibility of using the results for assessing the impact of competition, and for finding 'niche' markets in which an insurer can operate both competitively and profitably.

Premium analysis for copula model: A case study for Malaysian motor insurance claims

“…Table (3) shows the risk premium for independent and dependent models, whereas Table (4) provides the risk premium based on actual claims experience. Risk premiums for both independent and dependent models are calculated using (1). Under independent model, claim severities for each category are fitted separately to gamma regression models, whereas under dependent model, claim severities for all categories are fitted together using copula (normal and t copula from Elliptical family, and Frank, Clayton and Gumbel copula from Archimedean family) with gamma regression marginals.…”

“…Risk premium for the i-th risk class, i=1,2,…,n, can be equated as the product of estimated claim frequency and estimated average claim cost (severity) for all claim categories [1][2][3][4][5]. As such, if we have three claim categories, the risk premium is…”

Applications of Statistics in the Field of General Insurance: An Overview

“…Boland, 2007;De Jong & Heller, 2008;Ohlsson & Johansson, 2010). GLMs were introduced in actuarial sciences only by the end of the 20th century (Brockman & Wright, 1992;Haberman & Renshaw, 1996;Murphy et al, 2000). The typical data at disposal consists of claim information for a number of policies (from a few hundreds of thousands to over a few millions) over a number of years (5 to 10 years) and a number of explanatory variables (e.g.…”

Generalized Linear Models and Actuarial Science

“…The use of GLMs in this context appears to have its origin in the work of Baxter et al (1980), Coutts (1984) and McCullagh andNelder (1983, 1989). For a discussion of both actuarial and statistical aspects, see Brockman and Wright (1992).…”