Dependence Concepts, Stein's Identity and Conditional Expectation: A Theoretical Analysis and Exploration of Applications in Finance and Insurance (FWOTM806)

Our research group designs and conducts quantitative analyses to identify or improve solutions to problems in the areas of finance and insurance. The project falls into two parts. The first part studies how certain financial instruments (e.g., stocks, bonds, diversified portfolios etc.) interact with each other and to identify quantitative ways of assessing these correlations. Such research has the potential to help investors and regulators to quantify the risks that apply in worst case scenarios, such as global financial crises, and to formulate optimal strategies under various market conditions. We also investigate and develop the theories underlying these applications. Hence, our goal is to construct more realistic, versatile and practical models than those currently available. Moreover, we develop fast and accurate evaluation methods for certain option pricing problems in the market. Such methods are of immense value to industry professionals because a vast number of options are traded every day, and the pricing of these options can be very difficult. The second part is devoted to study a mathematical identity known as Stein’s lemma, which figures prominently in many problems in statistics. We generalize the classic results and apply them to the problem of optimal portfolio selection. Concrete ideas are developed in both parts, some of which are already in draft. Overall, we consider this area and our specific work to represent a fruitful and promising avenue of research.

Keywords:accounting

Disciplines:Business administration and accounting not elsewhere classified