C hapter#3 Insurance Benefits - PowerPoint Presentation

1. Chapter#3Insurance BenefitsSalma Alsuwailem

2. SummaryLife insurance benefits payable contingent upon death; payment made to a designated beneficiary -actuarial present values (APV) -actuarial symbols and notation Insurances payable at the moment of death -continuous -level benefits, varying benefits (e.g. increasing, decreasing) Insurances payable at the end of year of death -discrete -level benefits, varying benefits (e.g. increasing, decreasing) 2Salma Alsuwailem

3. ACTUARIL PRESENT VALUE(continuous)n-term life insurance An n-year term life insurance pays a benefit at EOY of death only if death occurs in the following n years. Because it does not cover the entire lifetime, it is cheaper than a whole life insurance with the same amount of benefit. Level Benefit Whole Life Insurance A whole life insurance pays a benefit at EOY of death of the policyholder, whenever it occurs. Pure endowmentAn n-year pure endowment provides a payment at the end of n years if the policyholder survives, but makes no payment if the policyholder dies within n years. Level Benefit Endowment Insurance An n-year endowment insurance provides an amount to be paid at EOY of death if death occurs in the next n years or at the end of year n if the policyholder survives to that time. Level Benefit Deferred Whole Life Insurance An n-year deferred whole life insurance pays a benefit at EOY of death if the policyholder has lived at least n years 3Salma Alsuwailem

4. ACTUARIL PRESENT VALUE(discrete)Insurances payable at EOY of death For insurances payable at the end of the year (EOY) of death, the PV r.v. Z clearly depends on the curtate future lifetime Kx. 4Salma Alsuwailem

5. Recursive relationships 5Salma Alsuwailem

6. For a special life insurance issued to (45), you are given:Death benefits are payable at the end of the year of death. The benefit amount is $100,000 in the in the first 10 years of death, decreasing to $50,000 after that until reaching age 65. An endowment benefit of $100,000 is paid if the insured reaches age 65. There are no benefits to be paid past the age of 65.Mortality follows the Standard Ultimate Life Table at i = 0.05. Calculate the actuarial present value (APV) for this insurance 6Salma Alsuwailemexamples

7. For an increasing 10-year term insurance, you are given: (i)  bk+1 =100,000(1+k),k=0,1,...,9 (ii)  Benefits are payable at the end of the year of death. (iii)  Mortality follows the Illustrative Life Table. (iv)  i = 0.06 (v)  The single benefit premium for this insurance on (41) is 16,736. Calculate the single benefit premium for this insurance on (40). (A) 12,700 (B) 13,600 (C) 14,500 (D) 15,500 (E) 16,300 7Salma Alsuwailem

8. For a special 3-year term insurance on (x), you are given: (i)  Z is the present value random variable for this insurance. (ii)  qx+k =0.02(iii)  The following benefits are payable at the end of the year of death: (iv)  i=0.06 Calculate Var(Z). (A) 9,600(B) 10,000(C) 10,400(D) 10,800(E) 11,200 8Salma Alsuwailemk bk+1 0 300 1 350 2 400

9. A decreasing term life insurance on (80) pays (20−k) at the end of the year of death if (80) dies in year k +1, for k = 0,1,2,...,19. You are given:(i) i = 0.06(ii) For a certain mortality table with q80 = 0.2, the single benefit premium for this insurance is 13.(iii) For this same mortality table, except that q80 = 0.1, the single benefit premium for this insurance is P.Calculate P.(A) 11.1 (B) 11.4 (C) 11.7 (D) 12.0 (E) 12.39Salma Alsuwailem

10. For a cohort of individuals all age x consisting of non-smokers (ns) and smokers (sm), you are given: • Mortality is based on the following:i=0.05= 0.0616 for a randomly chosen individual from this cohort Determine the proportion of non-smokers and smokers in this cohort at age x.  10Salma Alsuwailem

11. 11THANKS!Any questions?Salma Alsuwailem