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

该研究计划集中在两套相互联系和互补的定量金融研究计划：1）金融模拟，最优控制和数值方法; 2）或有资本证券研究。第一个项目侧重于具有提前行使特征的衍生证券的定价和风险管理的有效方法。这些技术对于金融机构和投资者的交易和内部风险管理流程以及确定满足内部和外部（监管）需求所需的资本水平都很重要。蒙特卡罗方法将被广泛研究，沿着还有其他一些适用于此类问题的数值方法。这项工作的结果有更广泛的应用，如金融投资组合管理，发电站的操作，并在大型系统，如一系列水库的维护的优化调度。

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.