Chapter 3. Modeling Loss Severity

Lead Author: Zeinab Amin, American University in Cairo

Chapter Preview. The traditional loss distribution approach to modeling aggregate losses starts by separately fitting a frequency distribution to the number of losses and a severity distribution to the size of losses. The estimated aggregate loss distribution combines the loss frequency distribution and the loss severity distribution by convolution. Discrete distributions often referred to as counting or frequency distributions were used in Chapter 2 to describe the number of events such as number of accidents to the driver or number of claims to the insurer. Lifetimes, asset values, losses and claim sizes are usually modeled as continuous random variables and as such are modeled using continuous distributions, often referred to as loss or severity distributions. Mixture distributions are used to model phenomenon investigated in a heterogeneous population, such as modelling more than one type of claims in liability insurance (small frequent claims and large relatively rare claims). In this chapter we explore the use of continuous as well as mixture distributions to model the random size of loss. We present key attributes that characterize continuous models and means of creating new distributions from existing ones. In this chapter we explore the effect of coverage modifications, which change the conditions that trigger a payment, such as applying deductibles, limits, or adjusting for inflation, on the distribution of individual loss amounts.