Ng Chi-Tim. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 110-114). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.4 / Chapter Chapter 2 --- Mathematical Background --- p.7 / Chapter 2.1 --- Fractional Stochastic Integral --- p.8 / Chapter 2.2 --- Wick's Calculus --- p.9 / Chapter 2.3 --- Malliavin Calculus --- p.19 / Chapter 2.4 --- Fractional Ito's Lemma --- p.27 / Chapter Chapter 3 --- The Fractional Black Scholes Model --- p.34 / Chapter 3.1 --- Fractional Geometric Brownian Motion --- p.35 / Chapter 3.2 --- Arbitrage Opportunities --- p.38 / Chapter 3.3 --- Fractional Black Scholes Equation --- p.40 / Chapter Chapter 4 --- Generalization --- p.43 / Chapter 4.1 --- Stochastic Gradients of Fractional Diffusion Processes --- p.44 / Chapter 4.2 --- An Example : Fractional Black Scholes Mdel with Varying Trend and Volatility --- p.46 / Chapter 4.3 --- Generalization of Fractional Black Scholes PDE --- p.48 / Chapter 4.4 --- Option Pricing Problem for Fractional Black Scholes Model with Varying Trend and Volatility --- p.55 / Chapter Chapter 5 --- Alternative Fractional Models --- p.59 / Chapter 5.1 --- Fractional Constant Elasticity Volatility (CEV) Models --- p.60 / Chapter 5.2 --- Pricing an European Call Option --- p.61 / Chapter Chapter 6 --- Problems in Fractional Models --- p.66 / Chapter Chapter 7 --- Arbitrage Opportunities --- p.68 / Chapter 7.1 --- Two Equivalent Expressions for Geometric Brownian Motions --- p.69 / Chapter 7.2 --- Self-financing Strategies --- p.70 / Chapter Chapter 8 --- Conclusions --- p.72 / Chapter Appendix A --- Fractional Stochastic Integral for Deterministic Integrand --- p.75 / Chapter A.1 --- Mapping from Inner-Product Space to a Set of Random Variables --- p.76 / Chapter A.2 --- Fractional Calculus --- p.77 / Chapter A.3 --- Spaces for Deterministic Functions --- p.79 / Chapter Appendix B --- Three Approaches of Stochastic Integration --- p.82 / Chapter B.1 --- S-Transformation Approach --- p.84 / Chapter B.2 --- Relationship between Three Types of Stochastic Integral --- p.89 / Reference --- p.90
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_324944 |
| Date | January 2004 |
| Contributors | Ng, Chi-Tim., Chinese University of Hong Kong Graduate School. Division of Risk Management Science. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, 114 leaves : ill. ; 30 cm. |
| Coverage | Europe |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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