Part5-Notes - Review Notes for Loss Models 1 - ACTSC...

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Review Notes for Loss Models 1 - ACTSC 431/831, FALL 2008 Part 5 – Aggregate Loss Models Roughly speaking, an aggregate loss model is used to describe the total loss of an insur- ance portfolio in a fixed time period. 1. Individual Risk Model: There are n policyholders in an insurance portfolio. Assume that policyholder i will produce a loss/claim of X i , i = 1 , 2 ,...,n. Then, the total or aggregate loss of the insurance is S n = X 1 + ··· + X n . Such an aggregate loss model is called the individual risk model. 2. Collective Risk Model: The number of claims in an insurance portfolio is a counting random variable N . The amount of the i th claim is X i , i = 1 , 2 ,... . Then the aggregate loss/claim of the insurance is S = X 1 + ··· + X N with S = 0 if N = 0. Such an aggregate loss model is called the collective risk model. Note that unless stated otherwise, in a collective risk model, we assume that N,X 1 ,X 2 ,... are independent and X 1 ,X 2 ,... have the same distribution function F ( x ) as X . Fur- thermore, we denote the probability function of N by p n = Pr { N = n } ,n = 0 , 1 , 2 ,.... (a) The distribution function of S is given by, for any x , F S ( x ) = Pr { S x } = X n =0 Pr { X 1 + ··· + X n x } p n = X n =0 p n F * n
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Part5-Notes - Review Notes for Loss Models 1 - ACTSC...

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