Titlebook: Life Insurance Theory; Actuarial Perspectiv F. Etienne Vylder Book 1997 Springer Science+Business Media Dordrecht 1997 development.differen

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particular, the present value ofA 00 and ä 00 is x x 0 0 2 A = ~ and ä = 1 + v + v + ... + v‘X resp. x x The price (or premium) of a time-capital is the expectation of its present value. In particular, the price ofA 00 and äx 00 is x 2 A = E(~) and ä = E(I + v + v + ... + v‘X) resp.978-1-4419-5189-2978-1-4757-2616-9

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Population Groups on a Graph,: .At any moment τ, any individual in state a can jump to a state β∈α′. The probability that this jump occurs during time interval dt equals .µ. dτ. Jumps akin to different individuals are independent. No individuals from outside join the graph and no individuals from the graph leave it.

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insurances at three different levels: time-capital, present value and price level. We call time-capital any distribution of a capital over time: (*) is the time-capital with amounts Cl, ~, ... , C at moments Tl, T , ..• , T resp. N 2 N For instance, let (x) be a life at instant 0 with future lifeti

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Financial Models,The . is the year. The . is any instant. It may be the subscription instant of some contract or the instant at which the insurer calculates the . (to be defined later) of some contract. The . is any amount (one dollar, one Swiss Franc,...).

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Construction of Life Tables,Life tables can be constructed for any large population group. We consider such a group of individuals with ages x≥ α, where α≥ 0 is a fixed initial age. Let the unknown life table of the group be .. (x≥ α). Then .and .where

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Life Annuities (One Life),The . (or . on the life x is the time-capital

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Life Insurances (One Life),The . on the life x is the time-capital

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Relations between Life Annuities and Life Insurances (One Life),By an integration by parts, .Hence,