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Life Insurance Theory - Actuarial Perspectives (Paperback, Softcover reprint of hardcover 1st ed. 1997)
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Life Insurance Theory - Actuarial Perspectives (Paperback, Softcover reprint of hardcover 1st ed. 1997)
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This book is different from all other books on Life Insurance by at
least one of the following characteristics 1-4. 1. The treatment of
life 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 lifetime X. Then the whole oO oO
life insurance A is the time-capital (I,X). The whole life annuity
a is the x x time-capital (1,0) + (1,1) + (1,2) + ... + (I,'X),
where 'X is the integer part ofX. The present value at 0 of
time-capital (*) is the random variable T1 T TN Cl V + ~ v , + ...
+ CNV . (**) In particular, the present value ofA 00 and a 00 is x
x 0 0 2 A = ~ and a = 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 ax 00 is x 2 A = E(~) and a =
E(I + v + v + ... + v'X) resp.
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