Recurrence Equations for Insurance Company Ruin Probabilities for Some Risk Models

Recurrentrelations are obtainedfor the ruinprobability calculations of aninsurance company in moments of insurance amounts. The problem is solved for two risk models. One of them is the classic Kramer—Lundberg model in which insurance amounts are distributed by an exponential law. In the second model random premiums and random insurance amounts are independent and also distributed by an exponential law. The number of premiums is a homogeneous Poisson process, and the claim moments take place in the same moments as the premium receiving, but the frequency of the claim moments is less than the premium receiving. The obtained relations alloy us to calculate the ruin probabilities in the infinite long time interval, and also to estimate for the first model and to calculate for the second model the ruin probabilities in the finite time interval.