The ruin problem described in section 3.4.1 is modified in the following way: The risk reserve process {R(t), t ≥ 0} is only observed at the end of each year. The total capital of the insurance...

The ruin problem described in section 3.4.1 is modified in the following way: The risk reserve process {R(t), t ≥ 0} is only observed at the end of each year. The total capital of the insurance company at the end of year n is

where x is the initial capital,K is the constant premium income per year, and  M_i
is the total claim size the insurance company has to cover in year i, M₀
= 0. The random variables M₁, M₂, ... are assumed to be independent and identically distributed as M = N(μ, σ²) with κ > μ > 3σ. Let p(x) be the ruin probability of the company, i.e. the probability that there is an n with property R(n) <>