Some new approximations for the density of the time to ruin

For a surplus process in actuarial risk theory, we obtain new approximations for the density of ruin time. These are found by choosing the best Gamma mixture and Normal mixture to a set of simulated ruin times and log-ruin times, respectively. The approach can be used in the classical and Sparre Andersen models of risk theory, but also in more general models, such as the classical model with diffusion. Although most of the results in the existing approximation methods require a light tail for claim sizes and/or a large value of the initial surplus, neither of these is needed in the current approach. We also obtain a formula for the exact asymptotic behavior of the ruin time density in the classical model with zero initial surplus.