General diffusions: financial applications, analysis and extension.

• Other Authors: Zhao, Jing
• Format: Others
• Language: English; Chinese
• Published: 2010
• Subjects: Diffusion processes > Mathematical models; Finance > Mathematical models; Options (Finance) > Prices > Mathematical models; Options (Finance) > Prices > United States > Mathematical models
• Online Access: http://library.cuhk.edu.hk/record=b6074923; http://repository.lib.cuhk.edu.hk/en/item/cuhk-344556

General diffusion processes (GDP), or Ito's processes, are potential candidates for the modeling of asset prices, interest rates and other financial quantities to cope with empirical evidence. This thesis considers the applications of general diffusions in finance and potential extensions. In particular, we focus on financial problems involving (optimal) stopping times. A typical example is the valuation of American options. We investigate the use of Laplace-Carson transform (LCT) in valuing American options, and discuss its strengthen and weaknesses. Homotopy analysis from topology is then introduced to derive closed-form American option pricing formulas under GDP. Another example is taken from optimal dividend policies with bankruptcy procedures, which is closely related to excursion time and occupation time of a general diffusion. With the aid of Fourier transform, we further extend the analysis to the case of multi-dimensional GDP by considering the currency option pricing with mean reversion and multi-scale stochastic volatility. === Zhao, Jing. === Adviser: Hoi-Ying Wong. === Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . === Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. === Includes bibliographical references (leaves 97-105). === Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. === Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. === Abstract also in Chinese.