Case 4 Background and Objective: Whether you know it or not, you are a “risk” in the eyes of insurance companies. If you are like most people — you’re not an Olympic athlete, and you don’t have serious health problems — then you are probably what is called a “standard risk”. Standard risk individuals qualify for an insurance company’s standard rates. Underwriting is the process by which a life insurance company decides which people to accept for insurance and on what terms. Then the main idea is that the risk premium covers the average risk. But if the premium is not adequate to the average risk, then the company will probably make a loss. The amount of extra risk then represents the underwriter’s assessment of how much worse the applicant is in mortality terms than a standard risk. An extra premium is an additional premium that the life insurance company charges on the top of its standard premium where an applicant is subject to an extra risk. Mortality cost is the biggest factor in your premium rates, and will be calculated by evaluating likelihood of dying during the policy. Your life insurance company will consider the following: health condition, age, gender, etc. One of the simplest types of insurance is Term life insurance. It is life insurance, which provides coverage at a fixed rate of payments for a limited period of time. After that period expires, coverage at the previous rate of premiums is no longer guaranteed and the client must either forgo coverage or potentially obtain further coverage with different payments or conditions. Perform insurance data analysis to determine the amount of premiums paid, what part of that amount should be kept in reserve to cover future liabilities, potential profit/loss, etc. Data: On September 7, 2014, MetLife LADT’s office have successfully issued 78 one year term life insurance contracts (InsuranceData.txt). Company’s actuaries and underwriters calculated annual premiums in the following way: Risk premium=Insurance amount × Death probability (depends on gender and age, see Mortality.xls) × (1+Extra risk factor). Based on the value of the extra risk factor, risk is classified into 4 categories: Extra risk = No risk, if Extra risk factor=0.0 Extra risk = Low risk, if 0.2>=Extra risk factor>0 Extra risk = Moderate risk, if 0.5>=Extra risk factor>0.2 Extra risk = High risk, if Extra risk factor>0.5 Insurance premium = Insurance amount × Death probability (depends on gender and age) × (1+Extra risk factor) + Policy fee, where the value of the policy fee (covers salaries for underwriters, office rent, utilities, administrative expenses, etc.) is based on extra risk level: Policy fee = 10, if No risk Policy fee = 15, if Low risk Policy fee = 20, if Moderate*risk Policy fee = 25, if High risk Death probabilities, based on age and gender, can be found in MortalityTable.xls. Each policy has insurance amount of $20,000. Questions: 1. What is the average risk premium based on the policies issued on September 7, 2012? 2. What is the average insurance premium based on policies issued on September 7, 2012? 3. Find the average insurance premium for different categories of “Extra risk” characteristic for males and females separately. Report the largest average insurance premium, and its corresponding “Extra risk” category and gender. Average of Insurance Premium Gender Risk Level Male High Risk 88.84 Low Risk 62.63 Moderate Risk 82.65 No Risk 49.21 Total 68.21 Average of Insurance Premium Gender Risk Level Female High Risk Low Risk Moderate Risk No Risk Total 4. Risk premiums help the company create technical provisions (reserves) to cover insurance events associated death risk. Of the 78 life insurance policies, would the reserve funds be sufficient to cover one death? If not, what is the solution to insure that the company has sufficient reserves to cover 1 death? Briefly explain. 5. Calculate the average insurance premium by age, gender and “Extra risk” characteristic. Report the triplet (age, gender and “Extra risk” characteristic) that corresponds to the largest average premium and provide the corresponding value. 6. Assume that all 78 policies will be renewed for one more year and that no one’s health condition has changed and that the insurance amount for each policy remained unchanged. The insurance company has decided to increase the policy fee by 10% for the next year. What is the total amount of risk premiums the company will collect during the second year?