An insurance company has an initial surplus of 100 and premium loading factor of 20%. Assume that claims arrive according to a Poisson process with parameter λ = 5 and the size of claims X₁ are iid random variables with X; ~ 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 occurs within 5 days after t'. Calculate also the probability that at least 2 claims occur within 5 days after t'. (b) Let t = 2 months. Calculate the mean and variance of S(t) and of U(t), where (S(r)) r2o and (U(r))r≥o are the aggregate claim process and the surplus process of the described model.
An insurance company has an initial surplus of 100 and premium loading factor of 20%. Assume that claims arrive according to a Poisson process with parameter λ = 5 and the size of claims X₁ are iid random variables with X; ~ 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 occurs within 5 days after t'. Calculate also the probability that at least 2 claims occur within 5 days after t'. (b) Let t = 2 months. Calculate the mean and variance of S(t) and of U(t), where (S(r)) r2o and (U(r))r≥o are the aggregate claim process and the surplus process of the described model.
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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Transcribed Image Text:An insurance company has an initial surplus of 100 and premium loading factor of 20%. Assume
that claims arrive according to a Poisson process with parameter \ 5 and the size of claims
Xį 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 occurs
within 5 days after t'. Calculate also the probability that at least 2 claims occur within 5
days 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 the
described model.
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