1. A Course in Financial Calculus
by Alison Etheridge
This text is designed for first courses in financial calculus aimed at students with a good background in mathematics. Key concepts such as martingales and change of measure are introduced in the discrete time framework, allowing an accessible account of Brownian motion and stochastic calculus. The Black-Scholes pricing formula is first derived in the simplest financial context. Subsequent chapters are devoted to increasing the financial sophistication of the models and instruments. The final chapter introduces more advanced topics including stock price models with jumps, and stochastic volatility. A large number of exercises and examples illustrate how the methods and concepts can be applied to realistic financial questions.
2. An Introduction in DiscreteTime
Editor-in-Chief: Marjorie Senechal
The Mathematical Intelligencer publishes articles about mathematics, about mathematicians, and about the history and culture of mathematics. Written in an engaging, informal style,* our pages inform and entertain a broad audience of mathematicians and the wider intellectual community.
We welcome expository articles on all kinds of mathematics, and articles that portray the diversity of mathematical communities and mathematical thought, emergent mathematical communities around the world, new interdisciplinary trends, and relations between mathematics and other areas of culture. Humor is welcome, as are puzzles, poetry, fiction, and art.
- An Introduction in Discrete Time.pdf
3. Elementary Probability Theory
作者: Kai Lai Chung / Farid Aitsahlia
This book provides an introduction to probability theory and its applications. The emphasis is on essential probabilistic reasoning, which is illustrated with a large number of samples. The fourth edition adds material related to mathematical finance as well as expansions on stable laws and martingales. From the reviews: "Almost thirty years after its first edition, this charming book continues to be an excellent text for teaching and for self study." -- STATISTICAL PAPERS
4. Interest Rate Models-Theory andPractice
by Damiano Brigo (Author), Fabio Mercurio (Author)
"The text is no doubt my favorite on the subject of interest rate modeling. It perfectly combines mathematical depth, historical perspective and practical relevance. The fact that the authors combine a strong mathematical (finance) background with expert practice knowledge (they both work in a bank) contributes hugely to its format. I also admire the style of writing: at the same time concise and pedagogically fresh. The authors’ applied background allows for numerous comments on why certain models have (or have not) made it in practice. The theory is interwoven with detailed numerical examples…For those who have a sufficiently strong mathematical background, this book is a must."
5. Introduction To StochasticCalculus With Applications
By (author): Fima C Klebaner (Monash University, Australia)This book presents a concise and rigorous treatment of stochastic calculus. It also gives its main applications in finance, biology and engineering. In finance, the stochastic calculus is applied to pricing options by no arbitrage. In biology, it is applied to populations' models, and in engineering it is applied to filter signal from noise. Not everything is proved, but enough proofs are given to make it a mathematically rigorous exposition.
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