Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar by Silvana Pesenti: Reverse Stress Testing: Static and Dynamic
Silvana Pesenti, Assistant Professor, Department of Statistical Sciences, University of TorontoUniversity of Toronto
Reverse Stress Testing: Static and Dynamic
This presentation is based on a collection of works that focus on the development of a mathematical framework for reverse stress testing. In the static setting, a model comprises of a vector of random input factors, an aggregation function mapping input factors to a random output, and a (baseline) probability measure. As is common in risk management, the value of the risk measure applied to the output is a decision variable. Therefore, it is of interest to associate a critical increase in the risk measure to a change in the baseline model. We propose a global and model-independent framework, termed “reverse stress testing”, comprising two steps: (a) an output stress is specified, corresponding to an increase in a risk measure(s) and (b) a (stressed) probability measure is derived, minimising a divergence to the baseline probability, under constraints generated by the output stress.
In the dynamic setting the model comprises of a stochastic process and a baseline probability measure. In an analogous fashion, the reverse sensitivity framework first specifies a stress on the distribution of the stochastic process at terminal time, and second derives the stressed probability measure that minimises, along the path, a divergence to the baseline probability. We characterise the unique solution to this optimisation problem, that is the stressed stochastic process closest to the baseline process that fulfills the stress.
Meeting ID: 817 7010 7418
Mathematical Finance, Stochastic Analysis, and Machine LearningZoom link