1. Under otherwise the same assumptions as made in example 3.22, determine the ruin probability the claim size if M has density 2. Claims arrive at an insurance company according to an ordinary...

1. Under otherwise the same assumptions as made in example 3.22, determine the ruin probability the claim size if M has density

2. Claims arrive at an insurance company according to an ordinary renewal process {Y₁, Y₂, ....}. The corresponding claim sizes M₁, M₂, ... are independent and identically distributed as M and independent of {Y₁, Y₂, ....}. Let the Y_i
be distributed as Y; i.e. Y is the typical interarrival interval. Then is the typical interarriv- (Y, M) al cycle From historical observations it is known that

Find approximate answers to the following problems:

(1) What minimum premium per unit time has the insurance company to take in so that it will make a profit of at least
 10⁶
within 10, 000 hours with probability α = 0.95 ?

(2) What is the probability that the total claim amount hits level
 4 ⋅ 10⁶
in the interval [0, 7,000 hours]?

(Before possibly reaching its goals the insurance company may have experienced one or more ruins with subsequent 'red number periods'.)