(1) Determine the ruin probability \(p(x)\) of an insurance company with an initial capital of \(x=\$ 20000\) and operating parameters

\[1 / \mu=2\left[h^{-1}\right], v=\$ 800 \text { and } \kappa=1700[\$ / h]\]

(2) Under otherwise the same conditions, draw the the graphs of the ruin probability for \(x=20000\) and \(x=0\) in dependence on \(\kappa\) over the interval \(1600 \leq \kappa \leq 1800\).

(3) With the numerical parameters given under (1), determine the upper bound \(e^{-r x}\) for \(p(x)\) given by the Lundberg inequality (7.85).

(4) Under otherwise the same conditions, draw the graph of \(e^{-r x}\) with \(x=20000\) in dependence on \(\kappa\) over the interval \(1600 \leq \kappa \leq 1800\) and compare to the corresponding graph obtained under (2).

Data from 7.85

Transcribed Image Text:

p(x)ex