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Unformatted text preview: Review Notes for Loss Models 1  ACTSC 431/831, FALL 2008 Part 6 The Classical ContinuousTime Ruin Model In this part, times are measured in years, unless stated otherwise . 1. Poisson Process: Let N t be the number of claims up to time t or the number of claims occurring in the time interval (0 , t ] , t > 0. The process { N t , t } is said to be a Poisson process with rate > 0 if the following three conditions hold: (a) N = 0 . (b) The number of claims in any time interval of length t has a Poisson distribution with mean t , namely, for all s 0 and t > 0, Pr { there are n claims in ( s, s + t ] } = Pr { N t + s N s = n } = ( t ) n e t n ! . (c) The process { N t , t } has stationary and independent increments. Stationary increments mean that for all n = 1 , 2 ,..., t < t 1 < < t n and h 0, the distribution of the random vector ( N t 1 + h N t + h , N t 2 + h N t 1 + h , , N t n + h N t n 1 + h ) does not depend on h . In particular, N t + h N h has the same distribution as N t . Independent increments mean that for all n = 1 , 2 ,..., t < t 1 < < t n , random variables N t 1 N t , N t 2 N t...
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This note was uploaded on 02/02/2010 for the course ACTSC 331 taught by Professor David during the Fall '09 term at Waterloo.
 Fall '09
 david

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