Pricing in General Insurance

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6

The Scientic Basis for Pricing: Risk Loss Models

and the Frequency/Severity Risk Costing Process

In Chapter 2, we looked at an extremely simplied, and old-fashioned, way of doing pricing,

by considering the total losses incurred in a policy over the years. By a series of enhance-

ments, this method can actually be developed to the point where it actually provides a

reasonable rst-cut indication of what the correct price may be, provided the loss experi-

ence is sufcient: this is the so-called burning cost analysis, which will be illustrated in

Chapter 11. However, to put pricing on a sound scientic basis, we need to understand and

model the loss-generation process itself.

In this chapter, we introduce the frequency/severity loss model as a useful method to

capture theoretically the loss-generation process. Section 6.1 (Aggregate loss models) is

devoted to studying the properties of the collective risk model and the individual risk

models and shows examples of situations in which they can be applied. Risk costing can

then be reformulated (Section 6.2) as the problem of nding the correct distribution of

claim counts (the frequency distribution) and of loss amounts (the severity distribution)

and the value of the necessary parameters. Section 6.3 illustrates the revised risk-costing

process based on the frequency/severity analysis.

6.1 Aggregate Loss Models

At the core of pricing, there is the building of a loss model. This is a model of how losses

are generated. And because we are mostly interested in the total losses incurred during the

policy period, we are interested in models for these aggregate losses. The main aggregate

loss models are the individual risk model and the collective risk model. We will devote

some time to both. A good in-depth reference for this material is Klugman et al. (2008).

6.1.1 Individual Risk Model

We have n risks on the book, and each of them has a probability p

1

, … p

n

of having a loss.

If a loss occurs, the amount could either be a random amount or a xed amount. Only one

loss is possible for each risk. The total losses for each year will then be

S = X

1

+ … + X

n

(6.1)

where X

j

is the loss for risk j, which will be = 0 if risk j has no loss.

We make the following two additional assumptions: that the loss events are indepen-

dent and that the severities are independent (but not necessarily identically distributed).

We can summarise all the assumptions as follows: