Measures of financial risk and derivative pricing

点击翻译按钮获取中文摘要

The objective of my research is to develop the mathematical models and theory for financial applications and to apply the results to financial markets. The topics include pricing and hedging derivative securities, measures of risk, and risk management.Measurement and management of financial risks are important topics in mathematical finance. I work on problems related to a "coherent risk measure". It is known that a coherent risk measure is described by a set of probability measures, in the sense that the future value is acceptable if and only if every expected value under probability measures in the set are nonnegative. When there is the possibility of dynamic trading or the evolution of available information, the need for multi-period risk measurement arises. This topic has been treated in the papers (with Artzner, Delbaen, Eber and Heath). Risk measures are widely applied to finance theory.I also work on pricing and hedging of complicated derivative securities. Since Black-Scholes formula provided a theoretical method of pricing and hedging derivatives, the mathematical theory has permitted the creation and pricing of numerous derivatives. In reality, a market is "incomplete". Pricing and hedging in such incomplete markets become more complex. The proposed research will provide financial institutions (such as banks) with the theoretical backgrounds and help them design specialized derivatives, find a "fair" price, and manage their risks.