Average Reviews:
(More customer reviews)This book is a textbook for the author's 2011 course "Numerical Methods" at the University of Technology. The style of the book is very similar to the author's other book, Benchmark Approach to Quantitative Finance. The mathematics covered in the book is fairly advanced, and mostly not used in the real world. Don't expect the book would land you a quant job. However, it is a good source for SDE in finance, very useful for mathematicians, researchers or anybody who just wants to solidify his knowledge in SDE.
Some of the topics covered in the book: stochastic Taylor expansions, SDE simulation, Monte-Carlo, FDM, filtering and more. You would ask why you would consider the book, given there have been a decent of other books covering similar contents. The answer is that the book is unique in the way that it bridges pure mathematics to financial application. What does that mean? Most maths books are very theoretical, they show you how to prove a theorem, but they don't tell you what the theorem really is, like how to apply it practically. On the other hands, most books on financial mathematics don't go too much depth in the maths. For example, you read about Monte-Carlo, you know how to write a Monte-Carlo in C++, but do you know how to speed up the convergence? Variance reduction methods? Good, but can you do even better? Do you know how to achieve arbitrary speed improvement? The book, Numerical Solution of Stochastic Differential Equations with Jumps in Finance will show you how.
Essentially, the book is a collection of research papers mostly written by the author himself. If you are up for technical challenges, this book is for you.
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In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.
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