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Nobody1111
May 10th 2007, 02:13 PM
Problem is taken from exams for Polish Actuaries from 10th October 2005, Exercice 1, General Insurance Mathematics. Here is the problem:

Damage which occurred in year t is liquidated:
- in the same year with probability 0.3
- in the next year with probabilitu 0.3
- in the year t+k (k>1) with probability 0.8 * (0.5)^k
We don't care in which period of the year the damage occurred - e.g. if one damage occurred on the 1st January and any other damage occurred on 30th December the probability that they are liquidated by the end of the k-th year is the same.
Let R(t) denotes the number of damages which were NOT liquidated at the end of the year t (R(t) consists both of the unliquidated damages which occurred in year t as well as of the unliquidated damages which occurred before the year t and weren't liquidated at the end of year t-1).
Let n(t) denotes the number of damages in year t.
Assuming that
R(t-1) = 1100
n(t) = 900
n(t-1) = 800
find the expected value of R(t) under the three conditions given above.