Over the years, randomization has proven to be a powerful tool in the modeling of risks on several levels: for computational purposes, in uncovering connections between different models, but also in the consideration and generation of physical and/or synthetic scenarios in risk management. A second, and in part connected, theme is the parsimonious and structure-preserving refinement of stochastic models via matrix-valued parameters, and related questions concerning the appropriate and effective dimension of models for a given purpose. This lecture will deal with various recent advances in these fields, and also illustrate concrete applications in insurance and finance, including the optimal design of reinsurance treaties and the probabilistic analysis of the profitability of blockchain mining.
