The SCROLLER-project studies the connections between stochastic analysis, risk theory and machine learning. Our results will be applied to risk management and reliability analysis with a focus on environmental variables as risk factors and models related to climate. The project consists of 4 scientific work packages: WP1 - Reinforcement learning and stochastic optimal control: We investigate whether it is possible to use the ideas and theoretical results from the stochastic maximum principle in connection with reinforcement learning. Can we draw inspiration from the martingale methods and the maximum principle theory of stochastic optimal control to relax the Markovian assumption of reinforcement learning? We will compare ML methods for stochastic optimal control problems (e.g., reinforcement learning and deep neural networks) to classical dynamic programming techniques. WP2 - Constrained risk management and connections to machine learning: We study an optimal consumption problem with a weighted value at risk constraint (WVaR) as well as other kinds of trading constraints (for instance no shortselling). We would also like to include the WVaR concept when doing risk analysis of stochastic networks. WP3 - Stochastic process modeling of degradation caused by environmental risk factors: We use self-exciting processes with positive jumps to model degradation caused by sporadic shocks with clustering behaviour. We will study the limiting process when the jump intensity increases at the same time as jump size decreases and compare this to the gamma process and the inverse Gaussian process. We also study optimal maintenance. WP4 - Augmented environmental contours: We extend environmental contours with the hope of contributing to better safety assessments of structures exposed to environmental risk factors. In particular, we study design optimisation with buffering and see how WVaR can be included in the environmental contour framework. We also include time in the model.
Project leader: Kristina Rognlien Dahl
Institution: Matematisk institutt