R Programming for Actuarial Science

25 Actuarial Risk Theory – An Introduction: Collective and Individual Risk Models

Peter McQuire

25.1 Introduction

library(MASS); library(moments); library(copula)

Remark 25.1 This chapter includes several calculations which involve simulations. The number of simulations run were often restricted in the interest of computational efficiency, although they have been tested by running a greater number of simulations than included in the text. The reader should ensure sufficient simulations are run which give results which have an acceptable level of stability.

In this chapter we will study models used to assess risks associated with short-term insurance contracts. Examples of such contracts, which typically provide insurance cover for one year or less, include car insurance policies, house insurance policies, and one-year term assurance policies. In contrast with longer-term policies such as whole life assurance (see Chapter 23), these short-term policies may either lapse at the end of the annual contract with no further premium payable, or be renewed, at which point another premium is paid in respect of the risk insured for the next period. Each annual premium is therefore in respect of the risk taken on for the following year. Contrast this with typical life assurance policies where the mortality risk increases throughout the policy as the policyholder gets older; generally these longer-term contracts require a fixed, level premium to be paid throughout the contract such ...