The aggregate claims in a collective risk model, S = X, from a risk group has...
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The aggregate claims in a collective risk model, S = X, from a risk group has a i=1 compound Poisson distribution, where the number of claims, N, follows a Poisson distribution with mean 500 and the individual claim amount X; (in pounds) has the distribution exp(-x/100) 100 N f(x) The insurer is considering effecting either an excess of loss reinsurance arrangement with re- tention level 100, or proportion reinsurance with retention level of 80%. Calculate the mean and variance of the insurer's aggregate claims under both of these reinsurance arrangements. [10 marks] , x > 0. (b) Suppose that the aggregate claims from a different collective risk model are also assumed to follow a compound Poisson distribution. However this time the Poisson parameters for individual policies are drawn from a Gamma distribution with mean 200 and variance 100. Show that the number of claims follows a negative binomial distribution and give the param- eters of this negative binomial distribution. The aggregate claims have mean m, hence find the mean aggregate claim amount. [6 marks] The aggregate claims in a collective risk model, S = X, from a risk group has a i=1 compound Poisson distribution, where the number of claims, N, follows a Poisson distribution with mean 500 and the individual claim amount X; (in pounds) has the distribution exp(-x/100) 100 N f(x) The insurer is considering effecting either an excess of loss reinsurance arrangement with re- tention level 100, or proportion reinsurance with retention level of 80%. Calculate the mean and variance of the insurer's aggregate claims under both of these reinsurance arrangements. [10 marks] , x > 0. (b) Suppose that the aggregate claims from a different collective risk model are also assumed to follow a compound Poisson distribution. However this time the Poisson parameters for individual policies are drawn from a Gamma distribution with mean 200 and variance 100. Show that the number of claims follows a negative binomial distribution and give the param- eters of this negative binomial distribution. The aggregate claims have mean m, hence find the mean aggregate claim amount. [6 marks]
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Related Book For
Quantitative Methods for Business
ISBN: 978-0324651751
11th Edition
Authors: David Anderson, Dennis Sweeney, Thomas Williams, Jeffrey cam
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