Regulation in the insurance market has increased greatly over the past four decades, and recent regulatory frameworks such as Solvency II have made simulations increasingly important. Monte Carlo simulations are often too inefficient to be used by themselves, and these Monte Carlo simulations begin to struggle when the complexity of insurance contracts increases. For that reason, there have been numerous suggested improvements to traditional MC methods such as the sample recycling method and a neural network method. This thesis will review various risk measures, the methods used to calculate them, and a detailed analysis of the neural network method and the sample recycling method. The sample recycling method and the neural network method will then be analyzed in detail, and a comparative analysis of the sample recycling method and the neural network method will be given. It was discovered that both the sample recycling method and the neural network method provide a large improvement in computational cost and overall run time with minor impacts on the accuracy. Thus, it was concluded that the sample recycling method is best suited for contracts where the inner loop estimations are particularly complex and the neural network is a general method that pairs well with complex input portfolios.