How is it possible to aggregate and measure dependent risks? This thesis deals with this question. Therefore, we will use joint probability distribution and two risk measures, Value-at-Risk and Expected Shortfall. Joint probability distributions consist of separate marginal distributions and a copula, which represents the dependence structure. On the one hand we want to consider the case, that the separate marginal distributions are given and we look for upper and lower bounds of the Value-at-Risk and Expected Shortfall. These bounds should be valid for all copulas. On the other hand, we want to consider a bivariate example and conduct two different numerical approaches to calculate the distribution: numerical integration and the Arbenz-Embrechts-Puccetti-Algorithm.