Lecture%207%20Annotated - Life Insurance and Superannuation...

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Life Insurance and Superannuation Models Week 7: Profit Testing April 9, 2011 1 / 29
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Week 7: Profit Testing Summary of Lecture Introduction to profit testing what is profit testing? uses of profit testing procedures for profit testing Illustrations of profit testing conventional products unit-linked products Summary measures of profits profit vector and profit signatures net present value profit margin References CT5 Chapters 10 and 11 ACTL3002: Week 7 2
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Profit Testing Profit testing refers to the process of assessing the profitability of an insurance contract in advance of it being written It is more difficult to assess profitability of life insurance business: Contracts are long-term A lot of uncertainties: longevity, mortality, investments, expenses First step is usually projecting the expected cash flows ACTL3002: Week 7 3
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Components of Expected Cash Flow In order to calculate expected cash flows, the following information is needed: Premiums to be paid and when they are to be paid Expenses and when they are incurred Contingent benefits payable under the contract e.g. death benefits, annuity payments, survival benefits for endowment Other possible benefits such as cash surrender values Other expected cash payments such as taxes Other expected cash receipts such as investment management fees The provisions for the contract. ACTL3002: Week 7 4
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The Revenue The revenue account for a life insurer is: (+) premium incomes (+) Investment income ( - ) expenses ( - ) benefit payments (death claims, maturities, surrenders) ( - ) increase in provisions (reserves) = profit gross of tax ( - ) taxes = net profit ACTL3002: Week 7 5
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Multiple Decrement Tables A multiple decrement table is a computational tool for dealing with a population subject to more than one independent decrement. Examples: Death and withdrawal (or surrender) Employed (while in service), retired, disability, death Assume there are m decrements. Some notation: ( al ) x : total living at age x ; ( ad ) k x : number of lives removed between x and x + 1 due to decrement k ; ( al ) x + 1 = ( al ) x - m s k = 1 ( ad ) k x ACTL3002: Week 7 6
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Multiple Decrement Tables cont. .. Probabilities: ( aq ) k x = ( ad ) k x / ( al ) x ( aq ) x = m s k = 1 ( aq ) k x ( ap ) x = 1 - ( aq ) x = 1 - m s k = 1 ( aq ) k x t ( ap ) x = ( al ) x + 1 / ( al ) x = ( ap ) x · ( ap ) x + 1 ··· ( ap ) x + t - 1 ACTL3002: Week 7 7
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x ( al ) x ( ad ) 1 x · · · ( ad ) m x ( aq ) 1 x · · · ( aq ) m x ( ap ) x · · · · · · · · · · · · · · · · · · · · · . . . . . . . . . . . . . . . . . . . . . · · · · · · · · · · · · · · For profit testing purposes, only the values of ( aq ) 1 x , ..., ( aq ) m x and ( ap ) x are what we need. ACTL3002: Week 7
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This note was uploaded on 06/12/2011 for the course ASB 1001,2522, taught by Professor Nicole during the One '09 term at University of New South Wales.

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Lecture%207%20Annotated - Life Insurance and Superannuation...

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