Suppose that the classical risk model applies. Let (U(t))+zo denote the surplus process, that is, U(t)=u+ct...
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Suppose that the classical risk model applies. Let (U(t))+zo denote the surplus process, that is, U(t)=u+ct - S(t), where the aggregate claims process (S(t))+zo is a compound Poisson process with Poisson parameter λ = 4. Assume that the premium income rate per time unit is c=16, where the time-unit is a day, and that u = 50. Assume that the individual claims, denoted by X₁, EN, are distributed according to a Gamma distribution X,~ T(2, 4). i. Check if the condition c> XE[X₁] on the premium income rate is satisfied. Why is this condition important? ii. Calculate the mean and the variance of S(8). iii. Calculate E(S(17) S(9)|S(5) > 23). iv. What is the average surplus process after 10 days? v. Write down an equation for the adjustment coefficient R and calculate the value of R. Using your answer, determine an upper bound for the ultimate probability of ruin using Lundberg's inequality. vi. Consider a new surplus process U given by U(t) = 50+10t - S(t). How does the ultimate ruin probability for Û compare to the one for U? Provide a proof of your answer. Suppose that the classical risk model applies. Let (U(t))+zo denote the surplus process, that is, U(t)=u+ct - S(t), where the aggregate claims process (S(t))+zo is a compound Poisson process with Poisson parameter λ = 4. Assume that the premium income rate per time unit is c=16, where the time-unit is a day, and that u = 50. Assume that the individual claims, denoted by X₁, EN, are distributed according to a Gamma distribution X,~ T(2, 4). i. Check if the condition c> XE[X₁] on the premium income rate is satisfied. Why is this condition important? ii. Calculate the mean and the variance of S(8). iii. Calculate E(S(17) S(9)|S(5) > 23). iv. What is the average surplus process after 10 days? v. Write down an equation for the adjustment coefficient R and calculate the value of R. Using your answer, determine an upper bound for the ultimate probability of ruin using Lundberg's inequality. vi. Consider a new surplus process U given by U(t) = 50+10t - S(t). How does the ultimate ruin probability for Û compare to the one for U? Provide a proof of your answer.
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i To check if the condition c EX is satisfied we need to calculate the expected value of X and compare it to the product of and EX Given that X follows a Gamma distribution with parameters 2 4 the exp... View the full answer
Related Book For
Applied Regression Analysis and Other Multivariable Methods
ISBN: 978-1285051086
5th edition
Authors: David G. Kleinbaum, Lawrence L. Kupper, Azhar Nizam, Eli S. Rosenberg
Posted Date:
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