Using the definitions below, we develop a method of keeping track of calendar years and quarters assuming that time is measured by the number of calendar quarters since the beginning of calendar year 0. We pretend there was a calendar year A.D. 0 immediately before the year A.D. 1. In fact, the year before A.D. 1 was 1 B.c. This unfortunate choice can be traced to a shortage of trained actuaries when the current system of naming calendar years was established.

Let iyq = Issue year and quarter for cell

c. Each cell will contain business for only one issue year and quarter. The quarter beginning closest to the issue date will be assigned the business. For example, all business issued from 16 November 2000 to 15 February 2001 will be assigned to the first quarter of 2001. This will allow us to use policy quarter per-unit-issued results to calculate calendar quarter results byq = Beginning year and quarter for the model; the year and end of quarter at which the model begins cyq = Calendar year and quarter. Model results will be calculated separately for each calendar year and quarter.

variable

(c, cyq) = Any of the quarterly per-unit-issued results calculated in Chapter 12, such as Prem, Comm, AcqExp, and so on. For example, Prem

(c, cyq) is the quarterly premium perunit-

issued for cell c in quarter cyq.

Combined year and quarter variables are calculated using formulas of the following form:

Combined year and quarter = 4 (Year) + Quarter, where Year is a number such as 2000 and Quarter ranges from | to 4.

This results in a time variable that ranges from 7,601 for the first quarter of 1900 to 8,401 for the first quarter of 2100. The four quarters of the year 2000 are numbered 8,001, 8,002, 8,003, and 8,004.

Issue year and issue quarter are combined into a single variable:

iyq = 4 (Issue year) + Issue quarter.

The beginning year and quarter for the model are combined into a single variable:

byq = 4 (Beginning calendar year) + Beginning calendar quarter.

The calendar years and quarters to be projected by the model are combined into a single variable that is used to keep track of time as the model progresses:
cyq = 4 (Calendar year) + Calendar quarter.
Determine values of iyg, byq, and cyq for a model with business issued between 16 February 2000 and 15 May 2000, with the model beginning at the end of the fourth quarter of 2000, and with results calculated through the end of 2001.