Some Methods Used in the Estimation of the Ruin Probability

The ruin probability of an insurance company is one of the main issues in actuarial mathematics. In the classical Poisson model of the risk theory there exist analytic expressions for the ruin probability, but in other risk models, there are not. For this, researchers try to find upper and lower bounds, and better approximations. In this paper, we discuss some methods of estimating it: De Vylder, Beekman-Bowers, Cramer-Lundberg, Grandell, Renyi, Tijms, Willmot, and the diffusion approximation which can be obtained approximating the risk process by a Brownian motion with drift.