An insurance company has a premium income of ($ 106080) per day. The claim sizes are iid
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An insurance company has a premium income of \(\$ 106080\) per day. The claim sizes are iid random variables and have an exponential distribution with variance \(4 \cdot 10^{6}\left[\$^{2}\right]\). On average, 2 claims arrive per hour according to a homogeneous Poisson process. The time horizon is assumed to be infinite.
(1) What probability distribution have the interarrival times between two neighboring claims?
(2) Calculate the company's ruin probability if its initial capital is \(x=\$ 20000\).
(3) What minimal initial capital should the company have to make sure that its ruin probability does not exceed 0.01 ?
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Related Book For 
Applied Probability And Stochastic Processes
ISBN: 9780367658496
2nd Edition
Authors: Frank Beichelt
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