Building Class-Level Experience Cells

Why Class-Level Experience Cells Matter

Classification analysis begins with a data organization task: decide which risks belong together and assemble comparable records for each group. A classification cell is not merely a row in a spreadsheet. It is a defined group of risks, identified by specified classification values, with exposure, premium, and loss records attached on a consistent basis. If the group definitions or the underlying records are inconsistent, later calculations can describe data errors rather than differences in risk.

A cell may be defined by one characteristic, such as territory, or by a combination, such as territory and construction type. The chosen record unit also matters. A policy, vehicle, building, or policy-period segment can be the appropriate unit, depending on how the product is rated and how experience is recorded. The unit must be stated before records are grouped.

Definition: A classification cell is a group of records sharing the same specified classification values. Each record must be represented at a defined grain, such as one policy-period or one insured vehicle-period. A cell key is the ordered set of classification values used to identify that group. Cell-level exposure, premium, and loss totals are sums of the corresponding amounts for the records assigned to the cell.

For example, if the selected dimensions are territory and building construction, a cell key might be “North territory, masonry.” The cell definition must also say how territory and construction are determined, what dates the classification applies to, and what happens when a value is unknown. Those decisions should be made consistently across the records being studied.

Choose the Record Grain and Cell Key

The grain is the level represented by one record. It should match the way the insured risk and its experience can be identified. A policy-period grain can be suitable when a policy covers one rating unit and its classification is stable during the period. If the policy covers several separately rated vehicles or locations, a single policy-level row may hide distinctions or repeat the same policy totals across multiple cells. In that situation, the source records need a more specific grain, or the study must define a defensible way to represent the covered units.

The cell key consists only of the selected classification dimensions, but the underlying data should retain the identifiers and dates needed to apply those dimensions and verify the totals. A practical record may include a policy or risk-unit identifier, the coverage period, the classification values effective during that period, exposure, premium, and loss. Keep identifying fields separate from the cell key: an identifier distinguishes records but does not create a classification dimension.

Classification values must describe the same period as the experience being summarized. If an address or other relevant characteristic changes during a policy period, a single unqualified value may not represent the whole period. The data process should follow a documented time rule, such as using effective-dated segments where the source records support them. Do not combine a classification value from one date with experience from a different date without a stated basis.

Worked Example: Building a Two-Dimension Cell Table

A hypothetical insurer reviews six policy-period records for a small commercial package. Each record is already stated on a consistent policy-period basis. The selected dimensions are territory and construction. Group the records into cells and reconcile exposure, premium, and incurred loss.

Record	Territory	Construction	Exposure	Premium ($)	Incurred loss ($)
1	North	Masonry	1.0	1,200	400
2	North	Frame	0.5	800	600
3	North	Masonry	0.5	700	300
4	South	Frame	1.0	1,500	900
5	South	Masonry	0.5	650	0
6	South	Frame	0.5	750	500

Method. Use the ordered pair (territory, construction) as the cell key. Records 1 and 3 share the key (North, masonry), so their totals are exposure $1.0+0.5=1.5$, premium $1{,}200+700=\$1{,}900$, and incurred loss $\$400+\$300=\$700$.

Record 2 is the only (North, frame) record, giving exposure $0.5$, premium $\$800$, and loss $\$600$. Record 5 is the only (South, masonry) record, giving exposure $0.5$, premium $\$650$, and loss $\$0$. Records 4 and 6 share (South, frame), giving exposure $1.0+0.5=1.5$, premium $\$1{,}500+\$750=\$2{,}250$, and loss $\$900+\$500=\$1{,}400$.

Cell key	Exposure	Premium ($)	Incurred loss ($)
North, masonry	1.5	1,900	700
North, frame	0.5	800	600
South, masonry	0.5	650	0
South, frame	1.5	2,250	1,400

Check. The cell exposures sum to $1.5+0.5+0.5+1.5=4.0$. Premium sums to $\$1{,}900+\$800+\$650+\$2{,}250=\$5{,}600$, and loss sums to $\$700+\$600+\$0+\$1{,}400=\$2{,}700$. These equal the six source-record totals. The common mistake this check avoids is assigning a record to two cells because it has two classification values; the combination of values defines one key.

Rules for Policies with Multiple Characteristics

A policy can have several characteristics that might appear relevant to a classification. A rule is needed to decide which value applies to each selected dimension. The rule should be objective, written down, and applied the same way to every record. “Use the territory recorded by the system” is not enough if systems or source fields disagree. A usable rule specifies the source and timing of the value, how conflicts are resolved, and how missing or ineligible values are handled.

The dimensions themselves also determine how to treat multiple covered units. If a policy covers distinct vehicles or locations that can occupy different cells, a policy-level record should not be copied into each of those cells with its full amounts. The study needs records at the relevant risk-unit grain, with the amounts attached to those units on a defensible basis. If the product instead has a policy-level classification rule, such as a designated principal location, apply that rule rather than assuming every characteristic creates another record.

Classification assignment and experience measurement must not be confused. A cell key answers “which group?” It does not, by itself, determine how to divide a policy’s premium or a claim’s loss among multiple risk units. Such amounts should be sourced or handled under a separately documented method; duplicating them is not a valid allocation.

Worked Example: A Policy with Several Possible Values

A hypothetical commercial vehicle policy has one insured vehicle for the full annual term. The vehicle is normally garaged at a North address, is occasionally parked at a South job site, and is used for both commuting and business deliveries. The study uses territory and use as its cell dimensions. Its written classification rules define territory by the vehicle’s principal garaging address and define use as business if the vehicle is used for any business delivery during the term. The policy record shows annual exposure of $1.0$, premium of $\$2{,}400$, and incurred loss of $\$900$.

Step 1: Apply the territory rule. The principal garaging address is North. The occasional South job-site parking does not override the stated principal-garaging rule, so the territory value is North.

Step 2: Apply the use rule. The vehicle makes business deliveries. Under the stated “any business delivery” rule, its use value is Business, even though it is also used for commuting.

Step 3: Form one cell key and record the amounts once. The key is (North, Business). This record contributes exposure $1.0$, premium $\$2{,}400$, and incurred loss $\$900$ to that cell. The values are not also placed in a (South, Business) or (North, Commuting) cell.

Check and trap avoided. The record’s full amounts appear once in the source totals and once in the selected cell. Choosing whichever location was most recently used, or assigning the policy to every observed combination, would contradict the defined rules and could duplicate experience.

Why the Cell Totals Reconcile

The basic justification for aggregating into cells is that a complete, nonoverlapping classification partitions the records. Let $x_i$ be any record-level quantity, such as exposure, premium, or loss. Let $I_{ic}=1$ if record $i$ belongs to cell $c$, and $I_{ic}=0$ otherwise. If every record belongs to exactly one cell, then $\sum_c I_{ic}=1$ for each record. Therefore:

\sum_c \sum_i I_{ic}x_i = \sum_i x_i\sum_c I_{ic} = \sum_i x_i.

The first expression sums the record quantities within each cell and then adds the cell totals. The last expression is the source total. Thus, if the cell assignment is exhaustive and nonoverlapping, grouping cannot change the overall total. A mismatch signals a problem such as an omitted record, a duplicated record, inconsistent filters, or an incorrect aggregation.

This identity applies separately to each quantity being summarized. It does not assert that every data field is suitable for every later analysis, or that the cell definitions are actuarially appropriate. It establishes a necessary bookkeeping check: the same set of records, measured on the same basis, should reconcile when grouped.

Worked Example: Finding a Duplicate in a Cell Extract

A hypothetical analyst prepares a two-cell extract from three valid policy-period records. The correct source records are: (East, 1.0 exposure, $\$1{,}000$ premium, $\$200$ loss), (West, 0.5 exposure, $\$600$ premium, $\$300$ loss), and (East, 0.5 exposure, $\$500$ premium, $\$100$ loss). During the extract, the first East record is accidentally included twice. Identify the issue and correct the totals.

Step 1: Compute the source totals. Exposure is $1.0+0.5+0.5=2.0$. Premium is $\$1{,}000+\$600+\$500=\$2{,}100$. Loss is $\$200+\$300+\$100=\$600$.

Step 2: Compute the faulty cell totals. East contains both East records plus a duplicate of the first: exposure $1.0+0.5+1.0=2.5$, premium $\$1{,}000+\$500+\$1{,}000=\$2{,}500$, and loss $\$200+\$100+\$200=\$500$. West contains exposure $0.5$, premium $\$600$, and loss $\$300$. The faulty extract therefore totals exposure $3.0$, premium $\$3{,}100$, and loss $\$800$.

Step 3: Correct the extract. Deduplicate using the valid policy-period record identifier, not merely matching amounts. The corrected East totals are exposure $1.0+0.5=1.5$, premium $\$1{,}000+\$500=\$1{,}500$, and loss $\$200+\$100=\$300$. West remains at $0.5$, $\$600$, and $\$300$. The corrected cell totals reconcile to $2.0$ exposure, $\$2{,}100$ premium, and $\$600$ loss.

The method is record-level deduplication followed by aggregation. The trap is to “fix” only the cell that looks unusual or to remove records based on equal dollar amounts; valid records can have identical amounts, so identifiers and transaction validity matter.

Practical Controls Before Analysis

A reliable cell extract should make its construction reproducible. Keep a record of the classification dimensions, the rule for each value, the observation period, the record grain, the treatment of missing values, and any exclusions. Then perform checks before interpreting cell differences.

Check the key space. List the possible combinations of selected values and identify combinations with no records. A missing combination is not automatically an error, but it should be distinguishable from a missing classification value.
Check uniqueness at the declared grain. Confirm that a record identifier and time period do not appear more than once unless the data structure explicitly permits multiple segments.
Check completeness. Count records with unknown or invalid values in each selected dimension. Do not silently drop them or assign them to a familiar class.
Check consistent measurement. Confirm that the exposure, premium, and loss fields cover the intended population and time basis. Do not combine figures drawn from different filters or periods without documenting the difference.
Reconcile totals. Compare cell sums with the totals for the same source records before drawing conclusions from the cells.

These controls matter because a classification table is the foundation for later calculations of class experience and relativities. A sparse cell, a missing value, or an unexpected total may indicate a real feature of the portfolio, a limitation in the data, or a processing error. The table alone cannot decide which explanation is correct; documentation and source checks are needed.

Key takeaway: Define the record grain, classification dimensions, and assignment rules before aggregating. A complete and nonoverlapping set of cell assignments preserves source totals; reconciliation is a basic test that the experience has been organized consistently.

Check Your Understanding

For each problem, identify the cell construction or data-control issue and check the final result.

A hypothetical study has three records classified by region and roof type: (Coastal, metal, 1.0 exposure), (Coastal, tile, 0.5 exposure), and (Inland, metal, 0.5 exposure). What are the three cell keys, and what is total exposure? (Answer: Coastal-metal, Coastal-tile, Inland-metal; total exposure $2.0$.)
A policy-level record has one full-term exposure of $1.0$, premium of $\$1{,}800$, and loss of $\$400$. It covers two separately rated vehicles in different territories. What is the valid conclusion about placing the policy-level amounts in territory cells? (Answer: The amounts cannot be copied in full to both cells; use vehicle-level data or a documented defensible allocation basis.)
A classification rule says to use the principal garaging territory. A vehicle is principally garaged in West but is temporarily parked in East for a week. Which territory value applies under this rule? (Answer: West.)
Four valid records have exposures $1.0$, $0.5$, $1.0$, and $0.5$. A cell extract sums to $3.5$. What should be checked first, and what is the correct source exposure total? (Answer: Check for duplicated records or inconsistent filters; the correct source total is $3.0$.)
A policy has a stable classification for the first half of a term and a different classification after a documented midterm change. What data structure is needed to avoid using one value for the whole term without justification? (Answer: Effective-dated policy-period segments aligned with the classification change.)

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