Loss Models: From Data to Decisions, 4th Edition

8.1 Introduction

We have seen a variety of examples that involve functions of random variables. In this chapter, we relate those functions to insurance applications. Throughout this chapter, we assume that all random variables have support on all or a subset of the nonnegative real numbers. At times in this chapter and later in the text, we need to distinguish between a random variable that measures the payment per loss (so zero is a possibility, taking place when there is a loss without a payment) and a variable that measures the payment per payment (the random variable is not defined when there is no payment). For notation, a per-loss variable is denoted Y^L and a per-payment variable is noted Y^P. When the distinction is not material (e.g., setting a maximum payment does not create a difference), the superscript is left off.