Final answer:
The question involves calculating the average territory rating factor for insurance risks using base rates, exposures, and claims frequency. The goal is to determine the expected premium for risk groups A, X, and Y, factoring in the ideal modifier which accounts for risk, and ultimately, ensuring the premiums cover claims, company costs, and profit.
Step-by-step explanation:
The student is asking about calculating the average territory rating factor for insurance risks that have maintained a claim-free status for 1 or more years. The process requires the application of various actuarial principles and a series of given formulas. It involves using the base rate, exposures, and claims frequency to determine the expected premium (EP) for specific risk groups, which in this case include A, X, and Y, at B rates.
The ideal modifier, which adjusts for risk, is also used in the process. Ultimately, the average territory rating factor is determined by dividing the EP at B rates by the product of exposures and the base rate at B rates for A+X+Y.
It's important to understand that in the insurance industry, ratings and premiums must, on average, cover the costs of claims, the costs of running the insurance company, and provide a profit for the firm.
This is due to the fundamental law of insurance which states that the payments received must cover all these costs over time, taking into account various factors such as investment income, administrative costs, and different risk profiles. The average territory rating factor is an aspect of insurance premium calculations that reflects the relative risk associated with a specific geographical area.