Book Description
Monte Carlo simulation has become an essential tool in the pricing of derivative securities and in risk management. These applications have, in turn, stimulated research into new Monte Carlo methods and renewed interest in some older techniques.
This book develops the use of Monte Carlo methods in finance and it also uses simulation as a vehicle for presenting models and ideas from financial engineering. It divides roughly into three parts. The first part develops the fundamentals of Monte Carlo methods, the foundations of derivatives pricing, and the implementation of several of the most important models used in financial engineering. The next part describes techniques for improving simulation accuracy and efficiency. The final third of the book addresses special topics: estimating price sensitivities, valuing American options, and measuring market risk and credit risk in financial portfolios.
The most important prerequisite is familiarity with the mathematical tools used to specify and analyze continuous-time models in finance, in particular the key ideas of stochastic calculus. Prior exposure to the basic principles of option pricing is useful but not essential.
The book is aimed at graduate students in financial engineering, researchers in Monte Carlo simulation, and practitioners implementing models in industry.
Mathematical Reviews, 2004: "... this book is very comprehensive, up-to-date and useful tool for those who are interested in implementing Monte Carlo methods in a financial context."
Customer Reviews:
Review for Monte Carlo Methods... by P. Glasserman.......2007-07-16
The book is just right for a reader who is looking for state-of-the-art techniques in Monte-Carlo methods in general. The fact that the book is specific to financial systems does not limit the usability of the book in the manner it is written. There are a lots of useful references one can get out of this book.
The book is for advanced readers in the sense that it requires rigorous mathematical ability to understand all the concepts. It is by no means for a novice reader and requires background in computational mathematics.
Best financial engineering book on MC.......2007-06-29
This is like the bible of Monte Carlo methods in financing. Both a good read and a good reference book. Must have! for any quant on wall street.
good book on Monte Carlo in Finance.......2007-04-02
But it seems the author is a little focused on selling his ideas, but not a very subjective overview of all topics in M-C method in finance.
Excelent choice on finance Monte Carlo.......2007-03-08
Clear and sound theoretical background on applied Monte Carlo for finance.
Brilliant.......2006-12-26
Almost everything related to Monte Carlo in Financial Engineering is covered at just the right level of detail. Quite easy to read too.
Book Description
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.
The theme of stochastic volatility also reappears systematically in the second part of the book, which has been revised fundamentally, presenting much more detailed analyses of the various interest-rate models available: the authors' perspective throughout is that the choice of a model should be based on the reality of how a particular sector of the financial market functions, never neglecting to examine liquid primary and derivative assets and identifying the sources of trading risk associated. This long-awaited new edition of an outstandingly successful, well-established book, concentrating on the most pertinent and widely accepted modelling approaches, provides the reader with a text focused on practical rather than theoretical aspects of financial modelling.
Customer Reviews:
Excellent introductory book to financial math.......2006-11-03
This book takes you through the math of finance step-by-step, passing through very simple examples first and then slowly adding complexity to the models studied. It is written very clearly and the prerequisites to reading this book are only some basic notions of probabilities (sigma-fields, probability measures).
Sometimes, the problem with math books is that they are "dry" and contain only a succession of theorems and proofs. In this one, the authors make a point of explaining in detail how different theorems and models relate to each other, and make extensive comparisons between them so that you get a better feel for how they work in practice.
The book is primarily a math book and can be light on market specifics. Do not buy this book as a practical "howto" in derivatives trading.
At the Forefront of Modern Mathematical Finance.......2005-05-23
This advanced text provides an excellent account of the current state-of-the art of options pricing/hedging models and interest rate term structure models. The book is accessible to both advanced practitioners of mathematical finance as well as to pure researchers in the field.
The book is in written in a mathematical style and contains rigorous proofs of many results. However, the main focus of the text is to describe the frontier of knowledge in the subject. Each section contains copious references to the literature and is so current that several references are to working papers. Many sections detail open problems and other areas suitable for scholarly research.
In their second edition, the authors provide an extremely useful critique of each modeling paradigm that they investigate. They also provide evidence for their position in the form of literature references which instruct the reader as to the shortcomings/limitations of a particular model. This information should prove quite valuable to model practitioners and implementers.
The authors assume an advanced background from the field of stochastic analysis, although they do provide an appendix which summarizes key results needed from the field. For the stochastic calculus prerequisites, I recommend Rogers & Williams "Diffusions, Markov Processes and Martingales" volumes I and II. Suitable prerequisites are also covered by Karatzas and Shreve in "Brownian Motion and Stochastic Calculus" 2nd edition. A good foundation in arbitrage pricing theory is also needed. I recommend the nice treatment by Bjork in "Arbitrage Theory in Continuous Time" 2nd edition.
The book is divided into two parts. The first part deals with options pricing in equity markets. Chapter 1 sets premlinaries required for the arbitrage theoretic framework, while Chapter 2 has a very nice treatment of discrete time models and finite financial markets.
In Chapter 3, the authors develop the Black-Scholes model along with the Bachelier model using arbitrage techniques. The models are compared and used as benchmark continuous time models and form the basis for all subsequent analysis.
Chapter 4 provides a nice survey of techniques used to price/hedge options in foreign equity and currency markets. The authors assume familarity of the basic workings of foriegn markets.
Chapter 5 is a terrific chapter on valuing American-style options. The American call option is thoroughly studied and approximation techniques for the American put option are introduced. The explicit derivations of the formulas are referenced to the literature.
Chapter 6 provides an introduction to exotic options, although the authors vary their use of the term 'exotic' to meaning 'not a standard European-style or American-style' in this chapter to meaning 'no readily available liquid market' in Chapter 7. The descriptions are quite accessible and the basic properties of the options are described along with pricing formulas (assuming the Black-Scholes framework).
Chapter 7 provides as complete an accounting as I have ever seen of the generalizations of the Black-Scholes model and motivates this from the point of view of volatility surfaces. Many of the well-known models are studied in detail, such as CEV, local volatility, and mixture models. The strengths and weaknesses of each model are analyzed. The stochastic volatility models of Wiggins (via Orenstien-Uhlenbeck processes), Hull-White, and Heston are studied, as is the SABR model. The chapter wraps up with a study of the SIV models, describes how the stochastic volatility models can be obtained via limits of GARCH models and surveys Jump-diffusion processes and Levy processes.
The second part of the book is concerned with term structure models and interest rate derivatives. The authors are quite well-know for their many contributions to this study and their treatment is authoritative.
Martingales & Finance.......2003-04-12
I have used this book for two courses in my MSc degree in Financial Maths...well this book is hard to understand at first glance, but, once you are introduced with a good course on stochastic analysis and applied probability, this is an illuminating book...I particularly enjoyed the part on foreing equity derivatives and exotic derivatives.....Harmed with patience this is definitely the book by which you can effectively gain a sound a knowledge on modern mathematical finance theory....reading in conjunction with Bingham-Kiesel book, could help understanding the foundation of the subject.
yes, but ..........2000-03-17
I've been using this book on and off over the last year. At first I was very impressed with the level of detail in the mathematics, especially as it was the only book at the time focussing on risk-neutral methods and covering BGM. But I've become increasing disillusioned with it of late. It's difficult to explain, but although the whole book is written in traditional theorem-proof style, there are no real proofs! (I have a PhD in math and have done research for 10 years so I should know a little about proofs.) The only "proofs" provided are basically symbol shifting, but the heart of the math is strangely absent. This is especially strange given the Springer series in which it appears.
In short, if you want a catalogue of methods this book does the job, but if you want a deeper understanding try Lars Nielsens book.
excellent book for post-John-Hull readers.......1999-08-17
This book covers essentially everything needed for a serious financial math study. It captures the spirit of modern financial math. For people with math, physics or engineering background, when you feel comfortable woth John Hull's books, then this book is right one, and a must one.
Book Description
Both in insurance and in finance applications, questions involving extremal events (such as large insurance claims, large fluctuations in financial data, stock market shocks, risk management, ...) play an increasingly important role. This book sets out to bridge the gap between the existing theory and practical applications both from a probabilistic as well as from a statistical point of view. Whatever new theory is presented is always motivated by relevant real-life examples. The numerous illustrations and examples, and the extensive bibliography make this book an ideal reference text for students, teachers and users in the industry of extremal event methodology.
Customer Reviews:
largest book written on extremes.......2002-01-30
This book presents extreme value theory and its applications with the finance industry as its primary target. There have been many excellent texts written on extreme value theory but none this extensive. As the authors admit even as extensive as it is the theory of multivariate extremes is neglected. They chose to only cover in detail the theory that is mature enough for application.
What you will find here that is not in many texts on this subject is a treatment of risk theory and fluctuations of sums and various time series models including cases with heavy-tailed marginal distributions.
Chapter 8 on special topics is particularly interesting with a lot of coverage for the extremal index, large claim index, ARCH processes, large deviations, reinsurance, stable processes and self-similarity. The book contains over 600 references to the literature and is a welcome resource for practitioners in finance and insurance as well as extreme value theorists.
Highly recommended.......2000-08-15
This book covers the theory and applications of extremal value theory (an area of applied probability). The mathematics is kept at an acceptable level, i.e. advanced undergraduates in math/physics/engineering, but the breadth and the sophistication of the statements are such that the results are never trivial. Chapters 2-3-4 introduce the reader to the property of sums, maxima and order statistics of random variables. Many results are only stated but not proved. Yet, this does not detract to the readability of the book. Chpater 5 treats point processes and requires a deeper mathematical background. Among the chapters, this was the most disappointing to me. The monographs of Resnick and of Kallenberg, as well as many good introductions to point processes in queueing theory, are in my opinion both a more intuitive and rigorous introduction to random measures. This is not a major flaw of the book, given its view toward applications; and besides this, the bibliographical notes will point the reader to the relevant literature. Chapter 6, on statistical analysis of extremal events, is enjoyable and extremely useful for practitioners in finance and insurance. Chapter 7 touches upon time series and its relation to heavy tails. Finally, chapter 8 is a put-pourri of topics: ARCH processes, stable processes, self-similarity. Overall, I found this book useful as a reference, but sometimes lacking in focus: some topics seem juxtaposed with no clear logical continuity. Another potential shortcoming of the book is that it is neither completely rigorous nor completely readable (i.e., an undergraduate-level book). At the same time, these can be considered as qualities: with regards to the former, there is plenty of material to consult and draw inspiration from; and at the same time each reader will find the "right" level of mathematics in the book. In my opinion the final balance is largely positive, and I would recommend this book without hesitation.
Book Description
The first part of this book presents the essential topics for an introduction to deterministic optimal control theory. The second part introduces stochastic optimal control for Markov diffusion processes. It also inlcudes two other topics important for applications, namely, the solution to the stochastic linear regulator and the separation principle.
Customer Reviews:
Be advised . . . .......2006-03-17
Not recommended as an introduction -- lacks examples.
Book Description
The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations, due to the peculiarities of stochastic calculus. The book proposes to the reader whose background knowledge is limited to undergraduate level methods for engineering and physics, and easily accessible introductions to SDE and then applications as well as the numerical methods for dealing with them. To help the reader develop an intuitive understanding and hand-on numerical skills, numerous exercises including PC-exercises are included.
Customer Reviews:
Excellent.......2002-04-10
This book is one of the finest written on the subject and is suitable for readers in a wide variety of fields, including mathematical finance, random dynamical systems, constructive quantum field theory, and mathematical biology. It is certainly well-suited for classroom use, and it includes computer exercises what are definitely helpful for those who need to develop actual computer code to solve the relevant equations of interest. Since it emphasizes the numerical solution of stochastic differential equations, the authors do not give the details behind the theory, but references are given for the interested reader.
As preparation for the study of SDEs, the authors detail some preliminary background on probability, statistics, and stochastic processes in Part 1 of the book. Particularly well-written is the discussion on random number generators and efficient methods for generating random numbers, such as the Box-Muller and Polar Marsaglia methods. Both discrete and continuous Markov processes are discussed, and the authors review the connection between Weiner processes (Brownian motion for the physicist reader) and white noise. The measure-theory foundations of the subject are outlined briefly for the interested reader.
Part 2 begins naturally with an overview of stochastic calculus, with the Ito calculus chosen to show how to generalize ordinary calculus to the stochastic realm. The authors motivate the subject as one in which the functional form of stochastic processes was emphasized, with Ito attempting to find out just when local properties such as the drift and diffusion coefficients can characterize the stochastic process. The Ito formula is shown to be a generalization of the chain rule of ordinary calculus to the case where stochasticity is present. The authors are also careful to distinguish between "random" differential equations and "stochastic" differential equations. The former can be solved by integrating over differentiable sample paths, but in the latter one has to face the nondifferentiability of the sample paths, and hence solutions are more difficult to obtain. The authors give many examples of SDEs that can be solved explicitly, and prove existence and uniqueness theorems for strong solutions of the SDEs. And since ordinary differential equations are usually tackled by Taylor series expansions, it is perhaps not surprising that this technique would be generalized to SDEs, which the authors do in detail in this part. They also outline the differences between the Ito and Stratonovich interpretations of stochastic integrals and SDEs.
Part 3 is definitely of great interest to those who must develop mathematical models using SDEs. The authors carefully outline the reasons where Ito versus the Stratonovich formulations are used, this being largely dependent on the degree of autocorrelation in the processes at hand. The Stratonovich SDE is recommended for cases when the white noise is used as an idealization of a (smooth) real noise process. The authors also show how to approximate Markov chain problems with diffusion processes, which are the solutions of Ito SDEs. Several very interesting examples are given of the applications of stochastic differential equations; the particular ones of direct interest to me were the ones on population dynamics, protein kinetics, and genetics; option pricing, and blood clotting dynamics/cellular energetics.
After a review of discrete time approzimations in ordinary deterministic differential equations, in part 4 the authors show to solve SDEs using this approximation. The familiar Euler approximation is considered, with a simple example having an explicit solution compared with its Euler approximate solution. They also show how to use simulations when an explicit solution is lacking. The importance notions of strong and weak convergence of the approximate solutions are discussed in detail. Strong convergence is basically a convergence in norm (absolute value), while weak convergence is taken with respect to a collection of test functions. Both of these types of convergence reduce to the ordinary deterministic sense of convergence when the random elements are removed.
The discussion of convergence in part 4 leads to a very extensive discussion of strongly convergent approximations in part 5, and weakly convergent approximations in part 6. Stochastic Taylor expansions done with respect to the strong convergence criterion are discussed, beginning with the Euler approximation. More complicated strongly convergent stochastic approximation schemes are also considered, such as the Milstein scheme, which reduces to the Euler scheme when the diffusion coefficients only depend on time. The strong Taylor schemes of all orders are treated in detail. Since Taylor approximations make evaluations of the derivatives necessary, which is computational intensive, the authors discuss strong approximation schemes that do not require this, much like the Runge-Kutta methods in the deterministic case , but the authors are careful to point out that the Runge-Kutta analogy is problematic in the stochastic case. Several of these "derivative-free" schemes are considered by the authors. The authors also consider implicit strong approximation schemes for stiff SDEs, wherein numerical instabilities are problematic. Interesting applications are given for strong approximations for SDEs, such as the Duffing-Van der Pol oscillator, which is very important system in engineering mechanics and phyics, and has been subjected to an incredible amount of research.
More detailed consideration of weak Taylor approximations is given in part 6. The Euler scheme is examined first in the weak approximation, with the higher-order schemes following. Since weak convergence is more stringent than strong convergence, it should come as no surprise that fewer terms are required to obtain convergence, as compared with strong convergence at the same order. This intuition is indeed verified in the discussion, and the authors treat both explicit and implicit weak approximations, along with extrapolation and predictor-corrector methods. And most importantly, the authors give an introduction to the Girsanov methods for variance reduction of weak approximations to Ito diffusions, along with other techniques for doing the same. Those readers involved in constructive quantum field theory will value the treatment on using weak approximations to calculate functional integrals. The approximation of Lyapunov exponents for stochastic dynamical systems is also treated, along with the approximation of invariant measures.
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Random Iterative Models (Stochastic Modelling and Applied Probability)
Marie Duflo
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ASIN: 3540571000 |
Book Description
The recent development of computation and automation has lead to quick advances in the theory and practice of recursive methods for stabilization, identification and control of complex stochastic models (guiding a rocket or a plane, organizing multiaccess broadcast channels, self-learning of neural networks ...). This book provides an up-to-date view of a wide range of those methods: stochastic approximation, linear and non-linear models, controlled Markov chains, estimation and adaptive control, learning ...Mathematicians (researchers and also students) and engineers will find here a self-contained account of many approaches to those theories.
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Random Walks in the Quarter-Plane: Algebraic Methods, Boundary Value Problems and Applications (Stochastic Modelling and Applied Probability)
Guy Fayolle ,
Roudolf Iasnogorodski , and
Vadim Malyshev
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ASIN: 3540650474 |
Book Description
This monograph aims at promoting original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes are of interest in several areas of mathematical research and are encountered in pure probabilistic problems, as well as in applications involving queuing theory. Using Riemann surfaces and boundary value problems, the authors propose completely new approaches to solve functional equations of two complex variables. These methods can also be employed to characterize the transient behavior of random walks in the quarter plane.
Book Description
Stochastic Subsurface Hydrogeology is the study of subsurface, geological heterogeneity, and its effects on flow and transport process, using probabilistic and geostatistical concepts. This book presents a rational, systematic approach for analyzing and modeling subsurface heterogeneity, and for modeling flow and transport in the subsurface, and for prediction and decision-making under uncertainty. The book covers the fundamentals and practical aspects of geostatistics and stochastic hydrogeology, coupling theoretical and practical aspects, with examples, case studies and guidelines for applications, and provides a summary and review of the major developments in these areas.
Customer Reviews:
A great book.......2004-09-17
This is a great book, for sure the best and most comprehensive book on stochastic hydrogeology available today. It covers nearly all the fundamental and practical aspects of stochastic hydrogeology, with emphasis on both the theoretical and practical aspects of the discipline. The language is simple, with many examples and case studies. The book is a great reference for scientists who are familiar with stochastic hydrogeology as well as for students and/or practitioners who may get informed about the discipline and learn how to implement the various tools available. The book is at the same time a very good introduction to the matter and a reference book for people who are already familiar with stochastic hydrogeology and want to keep updated with the most recent developments. This is the kind of book to keep on the desk.
An excellent textbook!.......2004-06-20
Applied Stochastic Hydrogeology is easily the best book of this century in its field. Its intuitive and down-to-earth style makes even the most intricate aspects of stochastic analyses readily accessible to both graduate students and active researchers. The subjects the book covers range from stochastic site characterization and image reconstruction from sparse data to the concept of effective hydraulic parameters and probabilistic assessment of flow and transport in heterogeneous environments.
Average customer rating:
- an essential reference for mdp researchers
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Competitive Markov Decision Processes
Jerzy Filar , and
Koos Vrieze
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Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization
ASIN: 0387948058 |
Book Description
This book is devoted to a unified treatment of Competitive Markov Decision Processes. It examines these processes from the standpoints of modeling and of optimization, providing newcomers to the field with an accessible account of algorithms, theory, and applications, while also supplying specialists with a comprehensive survey of recent developments. The treatment is self-contained, requiring only some knowledge of linear algebra and real analysis. Topics covered include: Mathematical programming: Markov decision processes (the non-competitive case), and stochastic games via mathematical programming.- Existence, structure and applications: Summable stochastic games, average-reward stochastic games and applications and special classes of stochastic games.- Appendices on: matrix games, bimatrix games and nonlinear programming; a theorem of Hardy and Littlewood; Markov chains; and complex varieties and the limit discount equation.
Customer Reviews:
an essential reference for mdp researchers.......2000-04-26
This book is an essential for anyone interested in Markov Decision Processes. It offers a rigorous introduction to MDPS and stochastic games. Also covered are various extensions and solution algorithms, as well as recent developments. Yet another nice yellow S-V book to add to your collection!
Book Description
This book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. The authors approach stochastic control problems by the method of dynamic programming. The text provides an introduction to dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. A new Chapter X gives an introduction to the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets. Chapter VI of the First Edition has been completely rewritten, to emphasize the relationships between logarithmic transformations and risk sensitivity. A new Chapter XI gives a concise introduction to two-controller, zero-sum differential games. Also covered are controlled Markov diffusions and viscosity solutions of Hamilton-Jacobi-Bellman equations. The authors have tried, through illustrative examples and selective material, to connect stochastic control theory with other mathematical areas (e.g. large deviations theory) and with applications to engineering, physics, management, and finance. In this Second Edition, new material on applications to mathematical finance has been added. Concise introductions to risk-sensitive control theory, nonlinear H-infinity control and differential games are also included.
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