Credit portfolio management applications require a mathematical model for a vector of random future time points, interpreted as default times of (possibly dependent) credit-risky assets. We advocate the use of a min-stable multivariate exponential (MSMVE) distribution as a natural candidate for this modeling task. The present article sheds light on the theoretical foundation that is required to accomplish this. It shows how to specify high-dimensional, low-parametric MSMVEs, and how to simulate them efficiently on a standard PC. The approach relies on a novel stochastic representation for MSMVEs based on so-called strong IDT processes.