Line of Business

Study guides: Exam 5, Exam 8, Exam 9

Line of Business is a grouping of policies covering a similar kind of risk that share an exposure base, a rating structure, a development pattern and a regulatory classification — personal auto, homeowners, workers compensation, commercial general liability, and so on. The line is the outermost level at which rate indications and reserve analyses are organized.

\text{Rate}_{\text{line}} = \frac{\text{Losses} + \text{LAE} + \text{Fixed Expenses}}{\text{Exposures} \times (1 - V - Q)}

• The line determines what the actuary can even measure: the exposure base, the relevant trends, the shape of the development pattern, and which rating variables are permitted.
• Lines differ along the axes tested in Types of Insurance — long vs. short tail, low vs. high frequency, occurrence vs. claims-made trigger — and each axis changes the choice of data organization and reserving method.
• Segmentation within a line (coverage, class, territory) balances Homogeneity against Credibility. Segmentation across lines is rarely optional: combining auto physical damage with general liability is indefensible on either criterion.
• Statutory reporting fixes the outer boundaries. Annual Statement Schedule P lines and NAIC line definitions determine how reserves are reported and how industry benchmarks are published, so the actuary's internal segments must roll up to them.
• Multi-line policies (commercial package, homeowners) are analyzed by coverage, not by policy, then recombined — a homeowners indication is built from separate property, liability and theft analyses.

Matching Exposure Base and Method to the Line An actuary must set up analyses for personal auto physical damage, workers compensation, and commercial general liability.

Specify the exposure base, aggregation basis and preferred reserving method for each.

Answer

	Auto phys. dam.	Workers comp	CGL
Exposure base	car-years	payroll per \$100	sales / receipts
Inflation-sensitive base?	no	yes → Exposure Trend	yes
Tail	short	long	long
Trigger	occurrence	occurrence	occurrence or claims-made
Aggregation	Accident Year	accident year	accident or Report Year
Reserving	chain ladder (paid)	BF at early ages	BF / Cape Cod

Nothing here is arbitrary: the tail dictates the reserving method, the base's inflation sensitivity dictates whether exposure trend applies, and the trigger dictates the aggregation basis.

Segmenting Inside a Line A homeowners book of \$80{,}000{,}000 is written across one state, with a large coastal territory exposed to hurricane.

How should the line be segmented for the rate indication?

Answer By coverage first, peril second, territory third.

1. Split the indication into property and liability (Section II) — different pure premiums, different development, different trends. Liability is a small slice of homeowners premium but a long-tail one.
2. Within property, pull out catastrophe losses. Hurricane losses are not projectable from five years of history; they are priced from a model's long-run average annual loss and loaded separately, while the non-catastrophe experience carries the rest of the indication.
3. Only then split by territory and amount of insurance for the relativities — those are a different exercise from the overall level, and each cell must be credibility-weighted.

The order matters. Territory relativities computed on catastrophe-inclusive data would swing wildly depending on whether a hurricane happened to hit the coastal territory during the experience period.