Part5-Notes-431-2011-F

Part5-Notes-431-2011-F - Review Notes for Loss Models 1 -...

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Review Notes for Loss Models 1 - ACTSC 431/831, FALL 2011 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. A common example of the individual risk model is that X i = B i I i , where I i = 1 , policyholder i makes claims , 0 , otherwise , and B i > 0 is the total amount of claims by policyholder i if it makes claims, i = 1 ,...,n. Thus, S n = B 1 I 1 + ··· + B n I n . 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
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Part5-Notes-431-2011-F - Review Notes for Loss Models 1 -...

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