Stochastic control and optimal stopping models for risk management

本项目致力于经济学和金融学中用于风险量化的随机控制和最优停止问题的设计和理论/数值研究。例如，考虑按照随机动力学X演化的资产的持有者。在这种情况下，持有资产的风险的概念可以通过测量当前资产的价值和其历史最大值S之间的距离S来给出。然后，投资者出售资产(和/或随后再次购买)的决定可以被视为基于对二维过程(X，S)的顺序观察而做出的时机决定(最优停止)。该项目的总体目标是开发概率/分析方法，以解决涉及一维扩散及其运行的最大/最小过程的广泛类别的停止/控制问题。该项目建立在该领域现有成果的基础上，旨在从单一代理人扩展到博弈论设置。可以考虑以部分和不对称信息为特征的上述问题的版本。主题和方法与EPSRC区域统计和应用概率保持一致。

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.