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...
Related questions
Question
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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 47 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON