An insurance company has an initial surplus of 100 and premium loading factor of 20%. Assumethat claims arrive according to a Poisson process with parameter \ 5 and the size of claimsXį are iid random variables with Xi exp(). The time unit is 1 week. Assume that 1 month=is 4 weeks.(a)Calculate the average number of claims on any given day, week and month.Let t'> 0 be an instance of time. Calculate the probability that at least one claim occurswithin 5 days after t'. Calculate also the probability that at least 2 claims occur within 5days after t'.(b)Let t = 2 months. Calculate the mean and variance of S(t) and of U(t), where(S(r))ro and (U(r))rzo are the aggregate claim process and the surplus process of thedescribed model.

An insurance company has an initial surplus of 100 and the premium loading factor is 20%.The claims…

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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