Stochastic control and optimal stopping models for risk management

This project is devoted to the design and theoretical/numerical study of stochastic control and optimal stopping problems for risk quantification in economics and finance. Consider for example the holder of an asset evolving according to a stochastic dynamics X. In this context, the notion of risk from holding the asset can be given by measuring the distance between the current asset's value and its historical maximum value S. The larger such distance the riskier the investor's position. Then, the investor's decision to sell the asset (and/or subsequently buy it again) can be cast as a timing decision (optimal stopping) based on the sequential observation of the two-dimensional process (X,S).
The overarching goal of the project is to develop probabilistic/analytical methods to address a broad class of stopping/control problems involving one-dimensional diffusions and their running maximum/minimum process. The project builds on existing results in the field and aims to extend from single-agent to game-theoretic setups. Versions of the above problems featuring also partial and asymmetric information may be considered.
The topic and methodology are aligned to the EPSRC area Statistics and Applied Probability.