Types of Insurance

Study guide: Exam 5

Types of Insurance, for ratemaking and reserving purposes, are distinguished less by what they cover than by three behavioural properties: how long claims take to report and settle, how frequent and how severe they are, and what triggers coverage. These three properties determine the data, the methods and the uncertainty of any analysis of the line.

\text{Pure Premium} = \text{Frequency} \times \text{Severity}

1. Tail length.

• Long-tail lines — medical malpractice, workers compensation, general liability, products, excess casualty — report and settle over many years, carry large IBNR, and are dominated by development uncertainty.
• Short-tail lines — auto physical damage, homeowners property, inland marine — are near ultimate within a year or two; the estimate is mostly known, and the risk is a catastrophe rather than development.

2. Frequency and severity.

• High frequency, low severity (auto physical damage, comprehensive): stable, credible experience; small samples suffice; chain ladder works well.
• Low frequency, high severity (excess liability, medical malpractice, property catastrophe): a handful of claims drives the result, so a single large loss can move a whole accident year and raw experience is rarely credible on its own.

3. Coverage trigger.

• Occurrence policies respond to losses occurring in the term, however late they are reported — so they generate pure IBNR and are organized on an Accident Year basis.
• Claims-made policies respond to claims reported in the term, so pure IBNR is nil, development is faster and Report Year is the natural cohort.

Reserve Sensitivity by Tail Length Two lines each show \$1{,}000{,}000 of reported losses at 24 months. Auto physical damage is 95\% reported at that maturity; medical malpractice is 30\% reported.

Compare the IBNR, and the effect of a 5\% error in the development factor.

Answer

\begin{align*}
\text{APD ultimate} &= \frac{\$1{,}000{,}000}{0.95} = \$1{,}052{,}600 \\
\text{APD IBNR} &= \$52{,}600 \\[6pt]
\text{Med mal ultimate} &= \frac{\$1{,}000{,}000}{0.30} = \$3{,}333{,}300 \\
\text{Med mal IBNR} &= \$2{,}333{,}300
\end{align*}

Now overstate each CDF by 5\%:

\begin{align*}
\Delta\text{APD} &= \$1{,}000{,}000 \times 1.0526 \times 0.05 \approx \$53{,}000 \\
\Delta\text{Med mal} &= \$1{,}000{,}000 \times 3.3333 \times 0.05 \approx \$167{,}000
\end{align*}

The same proportional error costs three times as much in the long-tail line, and it lands on a reserve that is itself 44 times larger. This leverage is the whole reason long-tail lines are reserved with multiple methods and reviewed against benchmarks.

Choosing a Method from the Line's Properties Classify each line and name the reserving method you would lean on at 12 months of maturity: (a) personal auto comprehensive, (b) a small book of architects' professional liability written claims-made, (c) commercial umbrella excess of \$1M.

Answer (a) Auto comprehensive — short-tail, high frequency, low severity, occurrence. Experience is credible almost immediately and development is nearly complete at 12 months, so the chain ladder on paid data is fine. Watch for hail catastrophes distorting a diagonal.

(b) Architects' E&O, claims-made — long-tail severity but no pure IBNR, small volume. Organize on Report Year; at 12 months use a BF estimate against an a priori loss ratio, because the claim count is too thin for chain ladder and IBNER dominates.

(c) Umbrella excess of \$1M — extremely long-tail, very low frequency, very high severity, occurrence. Almost nothing is reported at 12 months; a chain ladder factor there would be meaningless or undefined. Use the expected claims technique early, transitioning to BF and eventually chain ladder as the year matures, and price/reserve each large claim individually.