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# AVII.pdf

life actuarial

life actuarial

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### AVII.pdf

1. 1. Reserving Life Insurance Policy Alterations Complementary Insurance Universal Life Unit Linked Life Contingencies II Atuariado Vida II Gracinda R. Guerreiro Mestrado em Matemática Atuarial Life Contingencies II - FCT NOVA - 2021/22 Gracinda R. Guerreiro 1 / 14
2. 2. Reserving Life Insurance Policy Alterations Complementary Insurance Universal Life Unit Linked Program Part 1. Advanced Life Contingencies 1 Reserving Life Insurance 2 Policy Alterations 3 Complementary Insurance 4 Universal Life and Unit Linked Models Part 2. Construction of Mortality Tables 5 Estimation of Lifetime Distributions 6 Forecasting Mortality 7 Graduation Life Contingencies II - FCT NOVA - 2021/22 Gracinda R. Guerreiro 2 / 14
3. 3. Reserving Life Insurance Policy Alterations Complementary Insurance Universal Life Unit Linked – Part 1 – Advanced Life Contingencies Life Contingencies II - FCT NOVA - 2021/22 Gracinda R. Guerreiro 3 / 14
4. 4. Reserving Life Insurance Policy Alterations Complementary Insurance Universal Life Unit Linked Reserving Life Insurance Life Contingencies II - FCT NOVA - 2021/22 Gracinda R. Guerreiro 4 / 14
5. 5. Reserving Life Insurance Policy Alterations Complementary Insurance Universal Life Unit Linked Introduction • At the beginning of the contract (beginning of year 1), the present value of the insurer’s liabilities is equal to the value of the Insured’s liabilities (Actuarial Equivalence Principle). • With this condition of equivalence the pure premiums (single or annual) are determined. • In the end of year k (k = 1, 2, . . .), the present value of the Insurer’s liabilities is different from the present value of the Insured’s liabilities. • This equivalence would only remain unchanged over time if the payments being made by the policyholder correspond exactly to the risk being supported by the Insurer. Life Contingencies II - FCT NOVA - 2021/22 Gracinda R. Guerreiro 5 / 14
6. 6. Reserving Life Insurance Policy Alterations Complementary Insurance Universal Life Unit Linked Introduction 0,00 € 50,00 € 100,00 € 150,00 € 200,00 € 250,00 € 300,00 € 350,00 € 400,00 € 450,00 € 500,00 € 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 Temporary Life Insurance Level Premium Risk Premium Life Contingencies II - FCT NOVA - 2021/22 Gracinda R. Guerreiro 6 / 14
7. 7. Reserving Life Insurance Policy Alterations Complementary Insurance Universal Life Unit Linked Introduction • Whether the contract is paid at a single premium or at leveled premiums, there is a mismatch between the cost of the guarantees given by the Insurer and the amount paid by the policyholder in each year of the contract. • The anticipation of payments by the insured induces the need for the insurer to set up a provision (or reserve) that will, later on the contract, cover payments by the policyholder, which are insufficient to cover the risk to which the insurer is subject. The difference between the future liabilities of the insurer and the policyholder (immediately prior to payment of the premium) is designated by Net Premium Reserve. Life Contingencies II - FCT NOVA - 2021/22 Gracinda R. Guerreiro 7 / 14
8. 8. Reserving Life Insurance Policy Alterations Complementary Insurance Universal Life Unit Linked Introduction Notation: In the following, let: – x: age of the insured – n: term of the contract – p: term of premium payments – kVx - Net Premium Reserve in the end of year k of the contract (immediately prior to the payment of the premium) – An−k x+k - present value of future liabilities of the insurer – Pn−k x+k - present value of future liabilities of the policyholder Life Contingencies II - FCT NOVA - 2021/22 Gracinda R. Guerreiro 8 / 14
9. 9. Reserving Life Insurance Policy Alterations Complementary Insurance Universal Life Unit Linked Prospective Method Prospective Method kVx = An−k x+k − Pn−k x+k Observations: • 0Vx = 0 • nVx = 0 Life Contingencies II - FCT NOVA - 2021/22 Gracinda R. Guerreiro 9 / 14
10. 10. Reserving Life Insurance Policy Alterations Complementary Insurance Universal Life Unit Linked Prospective Method Exercises Solve Exercise 1. Life Contingencies II - FCT NOVA - 2021/22 Gracinda R. Guerreiro 10 / 14