Studies in Simulation, Optimal Control, Risk Management and Contingent Capital

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This research plan centres on two sets of linked and complementary quantitative finance research programs: 1) simulation, optimal control, and numerical methods in finance; and 2) studies in contingent capital securities. The first project focusses on efficient methods for pricing and risk management of derivative securities with early exercise features. These techniques are important to financial institutions and investors for trading and internal risk management processes and also for determining required capital levels to satisfy both internal and external (regulatory) demands. Monte Carlo methods will be extensively studied, along with some other numerical methods suited for such problems. Results from this work have broader applications such as financial portfolio management, the operation of power generating stations, and the optimal scheduling of maintenance in large systems such as a series of reservoirs.