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Stochastic Calculus for Finance
This book introduces key results essential for financial practitioners by means of concrete examples and a fully rigorous exposition.
Portfolio Theory and Risk Management
A rigorous account of classical portfolio theory and a simple introduction to modern risk measures and their limitations.
High-Frequency Statistics with Asynchronous and Irregular Data
Ole Martin extends well-established techniques for the analysis of high-frequency data based on regular observations to the more general setting of asynchronous and irregular observations. Such methods are much needed in practice as real data usually comes in irregular form. In the theoretical part he develops laws of large numbers and central limit theorems as well as a new bootstrap procedure to assess asymptotic laws. The author then applies the theoretical results to estimate the quadratic covariation and to construct tests for the presence of common jumps. The simulation results show that in finite samples his methods despite the much more complex setting perform comparably well as methods based on regular data. About the Author: Dr. Ole Martin completed his PhD at the Kiel University (CAU), Germany. His research focuses on high-frequency statistics for semimartingales with the aim to develop methods based on irregularly observed data.
The Black–Scholes Model
The Black–Scholes option pricing model is the first and by far the best-known continuous-time mathematical model used in mathematical finance. Here, it provides a sufficiently complex, yet tractable, testbed for exploring the basic methodology of option pricing. The discussion of extended markets, the careful attention paid to the requirements for admissible trading strategies, the development of pricing formulae for many widely traded instruments and the additional complications offered by multi-stock models will appeal to a wide class of instructors. Students, practitioners and researchers alike will benefit from the book's rigorous, but unfussy, approach to technical issues. It highlights potential pitfalls, gives clear motivation for results and techniques and includes carefully chosen examples and exercises, all of which make it suitable for self-study.
Discrete Models of Financial Markets
An excellent basis for further study. Suitable even for readers with no mathematical background.
Credit Risk
This master's-level introduction to mainstream credit risk modelling balances rigorous theory with real-world, post-credit crisis examples.
Probability for Finance
Students and instructors alike will benefit from this rigorous, unfussy text, which keeps a clear focus on the basic probabilistic concepts required for an understanding of financial market models, including independence and conditioning. Assuming only some calculus and linear algebra, the text develops key results of measure and integration, which are applied to probability spaces and random variables, culminating in central limit theory. Consequently it provides essential prerequisites to graduate-level study of modern finance and, more generally, to the study of stochastic processes. Results are proved carefully and the key concepts are motivated by concrete examples drawn from financial market models. Students can test their understanding through the large number of exercises and worked examples that are integral to the text.
Probability for Finance
A rigorous, unfussy introduction to modern probability theory that focuses squarely on applications in finance.
Stochastic Interest Rates
Designed for Master's students, this practical text strikes the right balance between mathematical rigour and real-world application.
Numerical Methods in Finance with C++
This book provides aspiring quant developers with the numerical techniques and programming skills needed in quantitative finance. No programming background required.
