Novel stochastic models in risk management and game theory

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Stochastic models have been found extremely useful to address various problems in quantitative finance and economics. However, recent developments in finance and economics led to new questions, such as, what suitable benchmarks in financial markets are, or how private information affects economic decisions. The aim of the proposed research is to address such questions in risk management and game theory by introducing new stochastic models and developing related mathematical tools in stochastics and control theory. The proposed research program consists of the following four parts. 1. Part: Trading and Equilibrium Models for Benchmarks Recent scandals over manipulation of price benchmarks on financial markets led to intense policy discussions on the design of such benchmarks. In the proposed research, we develop a mathematical framework that captures main criteria for suitability of benchmarks. 2. Part: Continuous-Time Games with Private Monitoring Firms often have both information from the market and their own private information while not directly observing other firms' actions. Such situations lead to so-called games with private monitoring. We plan to analyze such games in a continuous-time setting with different, correlated signals to model the different information of the firms. 3. Part: A Game-Theoretic Model for Banking Network Formation Since the financial crisis in 2007/8, the study of how banks are linked to each other via loans and financial derivatives has gained a lot of attention. In this part of the proposed research program, we develop a dynamic model to study how banks adjust their exposures between each other over time, leading to a formulation of repeated games on networks. 4. Part: Machine Learning in Credit Risk Management Techniques from machine learning are increasingly often applied by banks to estimate the credit risk of their individual customers. In this last part, we develop a mathematical framework that can be applied to make statistical inferences from data analytics on individual customers to aggregate risk measures, which are important in determining banks' capital requirements. The proposed research benefits Canada in three ways: its mathematical and statistical research community by developing novel stochastic models, its financial industry by providing a sound mathematical framework to address topical questions, and its students by giving excellent training opportunities in mathematical and statistical modelling of problems that are highly relevant in academia and industry.