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6. Introduction to StochasticIntegration

Authors: Kuo, Hui-Hsiung

The theory of stochastic integration, also called the Ito calculus, has a large spectrum of applications in virtually every scientific area involving random functions, but it can be a very difficult subject for people without much mathematical background. The Ito calculus was originally motivated by the construction of Markov diffusion processes from infinitesimal generators. Previously, the construction of such processes required several steps, whereas Ito constructed these diffusion processes directly in a single step as the solutions of stochastic integral equations associated with the infinitesimal generators. Moreover, the properties of these diffusion processes can be derived from the stochastic integral equations and the Ito formula.

7. Investment Science

作者: David G. Luenberger

Designed for those individuals interested in the current state of development in the field of investment science, this book emphasizes the fundamental principles and how they can be mastered and transformed into solutions of important and interesting investment problems. The book examines what the essential ideas are behind investment science, how they are represented, and how they can be used in actual investment practice. The book also examines where the field might be headed in the future, and goes much further in terms of mathematical content, featuring varying levels of mathematical sophistication throughout. End-of-chapter exercises are also included to help individuals get a better grasp on investment science.

8. Martingale Methods in FinancialModelling

作者: Marek Musiela / Marek Rutkowski

In the 2nd edition some sections of Part I are omitted for better readability, and a brand new chapter is devoted to volatility risk. As a consequence, hedging of plain-vanilla options and valuation of exotic options are no longer limited to the Black-Scholes framework with constant volatility. Applications to the valuation and hedging of American-style and game options are presented in some detail. The theme of stochastic volatility also reappears systematically in the second part of the book.

9. Mathematical Modeling andMethods of Option Pricing

by Lishang Jiang(Author)

From the unique perspective of partial differential equations (PDE), this self-contained book presents a systematic, advanced introduction to the Black–Scholes–Merton’s option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs. In particular, the qualitative and quantitative analysis of American option pricing is treated based on free boundary problems, and the implied volatility as an inverse problem is solved in the optimal control framework of parabolic equations.

10. Probability Essentials

Jacod J., Protter P

This introduction can be used, at the beginning graduate level, for a one-semester course on probability theory or for self-direction without benefit of a formal course; the measure theory needed is developed in the text. It will also be useful for students and teachers in related areas such as finance theory, electrical engineering, and operations research. The text covers the essentials in a directed and lean way with 28 short chapters, and assumes only an undergraduate background in mathematics. Readers are taken right up to a knowledge of the basics of Martingale Theory, and the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference.

11. Probability With Martingales

作者: David Williams

This is a masterly introduction to the modern and rigorous theory of probability. The author adopts the martingale theory as his main theme and moves at a lively pace through the subject's rigorous foundations. Measure theory is introduced and then immediately exploited by being applied to real probability theory. Classical results, such as Kolmogorov's Strong Law of Large Numbers and Three-Series Theorem are proved by martingale techniques. A proof of the Central Limit Theorem is also given. The author's style is entertaining and inimitable with pedagogy to the fore. Exercises play a vital role; there is a full quota of interesting and challenging problems, some with hints.

12. Solution of A Course inFinancial Calculus

13. Stochastic Calculus andFinancial Applications

14. Stochastic Calculus for Financei&ii

15. Stochastic Differential Equations

16. Term Structure Models: AGraduate Course

17. Theory of Financial Risk andDerivative Pricing

18. Time Series Analysis

19. Time series analysis and itsapplications with R examples

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