第一个书签之前
摘 要
Abstract
目 录
Contents
第 1 章 Introduction
1.1 Mathematical Principals and Brownian Motion
1.2 Numerical Methods for SDEs with Literature Review
1.2.1 Numerical Methods for OSDEs
1.2.2 Numerical Methods for SPDEs
1.3 Applications of SDEs in Finance
1.3.1 Background of Options Valuation
1.3.2 Applications
第 2 章 Two Classes of Split-step Theta Milstein Methods for OSDEs
2.1 Notations and Preliminaries
2.2 Drifting Split-step Theta Milstein Methods for OSDEs
2.2.1 Stability of the DSSM Methods
2.3 Improved Split-step Theta Milstein Methods for OSDEs
2.3.1 Stability of the MSSM Methods
2.4 Numerical Experiments
2.5 Summary
第 3 章 New Classes of s-stage Lobatto IIIC-Milstein methods for OSDEs
3.1 The Lobatto IIIC-Milstein Method
3.2 Convergence Properties
3.3 Stability Properties
3.3.1 Non-linear Stability
3.3.2 Liner Stability
3.4 Numerical Experiments
3.5 Summary
第 4 章 Split-step Theta Methods with Variable Step-Size for Stochastic Pantograph Differential Equations
4.1 Existence and Uniqueness
4.2 Moment Properties of SS Methods
4.3 Strong Convergence of SS Methods
4.4 Mean Square Stability of SS Methods
4.5 Numerical Experiments
4.6 Summary
第 5 章 Lobatto-Milstein Methods in Application of Uncertainty Investment for Solar Power Projects
5.1 Renewable Energy Sector in Egypt
5.2 The Lobatto IIIC-Milstein Method for OSDEs
5.3 The Real Option Framework
5.3.1 Framework Application
5.3.2 Stochastic Model
5.4 A Case Study: 140-MW Solar Power Plant in Kuraymat, Egypt
5.4.1 Estimate Discount Cash Flows
5.4.2 Estimate the Volatility
5.4.3 Valuation of the Deferred Option
5.4.4 Discussion of the Results
5.5 Summary
第 6 章 A stochastic corporate claim value model with variable delay
6.1 Definitions and Preliminary Results
6.2 Corporate Claims Model with Variable Delay
6.3 Evaluation debt and equity of a firm
6.4 Summary
结论与未来工作
Conclusion and Future Work
References
附录 A Background of the LobattoIIIC methods
List of Publications
Copyright
Acknowledgement
Resume
