Grant: Discovery Grants Program - Individual

In recent decades mathematics has begun to play an increasingly important role in the management of financial risk. This is true at all levels - from the retirement planning advice of financial advisors to the capital allocation decisions made by executives at the largest international financial institutions. Perhaps moreso than any other parameter, correlations between financial variables are critical inputs to any quantitative risk management model. Indeed the most natural form of risk management is diversification, and the efficacy of diversification depends crucially on correlations and relative volatilities. It is an empirical fact that correlations tend be highest during the most adverse economic scenarios (in other words, diversification is least effective when we need it the most), a phenomenon that is often referred to as state dependence, yet this fact is often either ignored or modeled in simple ways. The result is overly optimistic models that understate true risks.***The ultimate goal of the research program outlined here is to improve on the status quo in quantitative risk management, with particular emphasis on state dependence in correlations. Specific goals include (i) amassing a compelling body of quantitative evidence on the dangers of ignoring state dependence and (ii) developing models that allow for state dependence in correlations while simultaneously satisfying the needs of the modern financial institution (i.e. the models must be easy to understand and describe, as well as be straightforward to implement). In other words the goal is to convince risk management professionals that state dependence should be incorporated whenever possible, and then provide them with practical tools for doing so. It is expected that the majority of the students trained through this program will ultimately find employment in the financial sector, with many of up in some risk management function (at the present time, and in the aftermath of the financial crisis, risk management remains the most significant growth area in the financial sector). By exposing them to cutting-edge developments in quantitative risk management this program therefore has the potential to improve on the status quo, from the ground up.**