Chapter Preview. Many insurance datasets feature information about frequency, how often claims arise, in addition to severity, the claim size. This chapter introduces tools for handling the joint distribution of frequency and severity. Frequency-severity modeling is important in insurance applications because of features of contracts, policyholder behavior, databases that insurers maintain, and regulatory requirements. Model selection depends on the data form. For some data, we observe the claim amount and think about a zero claim as meaning no claim during that period. For other data, we observe individual claim amounts. Model selection also depends on the purpose of the inference; this chapter highlights the Tweedie generalized linear model as a desirable option. To emphasize practical applications, this chapter features a case study of Massachusetts automobile claims, using out-of-sample validation for model comparisons.

How Frequency Augments Severity Information

At a fundamental level, insurance companies accept premiums in exchange for promises to indemnify a policyholder on the uncertain occurrence of an insured event. This indemnification is known as a claim. A positive amount, also known as the severity, of the claim, is a key financial expenditure for an insurer. One can also think about a zero claim as equivalent to the insured event not occurring. So, knowing only the claim amount summarizes the reimbursement to the policyholder. Ignoring expenses, an insurer that examines only amounts paid would be indifferent to two claims of 100 when compared to one claim of 200, even though the number of claims differs.