In this dissertation we discuss the Ruin Theory, considering the classic collective risk model developed by Cramér and Lundberg, in which the number of claims that occur until a period of time t is modeled by a homogeneous Poisson process. We can say that an insurance company is in ruin if its reserve became negative at some instant t. The probability of this event to occur is called the ruin probability. Since it is difficult to find an explicit expression for the ruin probability of an insurance company, we present some numerical approaches for its estimation that are available in the literature. Also we show in this work how a reinsurance contract can alter the insurance company’s ruin probability. The effectiveness of the estimators of the ruin probabilities is verified with simulated data, where it is assumed different probabilist models for the claims.