Mathematics of Quantitative Risk Management under Uncertainty

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The recent economic crisis has led to a re-examination of the role of mathematics in finance in general, and risk management in particular. A lesson of paramount importance from this process of introspection has been the realization that both end users of models and the mathematicians who develop models need to pay more attention to the role of model uncertainty in the measurement and management of risk. The purpose of this project is to develop the underlying mathematics and practical tools necessary to facilitate the management of risk under model uncertainty. Two areas of application that will receive particular focus are counterparty credit risk (CCR) and insurance products with guarantees. Counterparty credit risk (CCR) refers to the risk of a loss due to an adverse change in the creditworthiness of a counterparty to an over-the-counter derivative contract. Its importance was dramatically illustrated by the devastation caused to the financial system by the default of Lehman brothers and the near default of AIG. CCR losses depend on both the timing of the adverse credit event (driven by credit risk factors), as well as the value of the portfolio of contracts when the event occurs (driven by market risk factors). Financial institutions often have in place models for market risk and credit risk separately; however, the joint modelling of these two risk types presents significant challenges, and the dependence structure in particular is a source of model uncertainty. Research will focus on deriving worst-case scenarios and conservative bounds for CCR given the uncertainty regarding the dependence between market and credit risk. Modern life insurance products have become increasing complex, offering numerous guarantees, and depending on many disparate sources of risk. Included among the risks a life insurer will face on its portfolio of guaranteed products are market (e.g. interest rate, equity) risk, mortality risk, and the risk associated with policyholder behaviour (e.g. lapse). Research on this topic will focus on two directions. The first will be the optimal behaviour for policyholders. Secondly, the impact of the insurer's decision making process on the policyholder will be studied.