Under the model assumptions of example 3.22, (1) determine the ruin probability p(x) of an insurance company with an initial capital of x =  20, 000 and operating parameters (2) with the numerical...

Under the model assumptions of example 3.22,

(1) determine the ruin probability p(x) of an insurance company with an initial capital of x =
 20, 000 and operating parameters

(2) with the numerical parameters given under (1), determine the upper bound e^{−r x}
of the Lundberg inequality (3.206),

(3) under otherwise the same conditions, draw the respective graphs of the ruin probability p(x) for x = 20, 000 and x = 0 (no initial capital) in dependence on over the interval 1600 ≤ κ ≤ 1800,