Functionals Of Multidimensional Diffusions With Applications To Finance

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Functionals of Multidimensional Diffusions with Applications to Finance

Jan Baldeaux,Eckhard Platen
Functionals of Multidimensional Diffusions with Applications to Finance Book PDF

Author : Jan Baldeaux,Eckhard Platen
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 54,6 Mb
Release : 2013-08-13
Category : Mathematics
ISBN : 9783319007472

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Functionals of Multidimensional Diffusions with Applications to Finance by Jan Baldeaux,Eckhard Platen Pdf

This research monograph provides an introduction to tractable multidimensional diffusion models, where transition densities, Laplace transforms, Fourier transforms, fundamental solutions or functionals can be obtained in explicit form. The book also provides an introduction to the use of Lie symmetry group methods for diffusions, which allows to compute a wide range of functionals. Besides the well-known methodology on affine diffusions it presents a novel approach to affine processes with applications in finance. Numerical methods, including Monte Carlo and quadrature methods, are discussed together with supporting material on stochastic processes. Applications in finance, for instance, on credit risk and credit valuation adjustment are included in the book. The functionals of multidimensional diffusions analyzed in this book are significant for many areas of application beyond finance. The book is aimed at a wide readership, and develops an intuitive and rigorous understanding of the mathematics underlying the derivation of explicit formulas for functionals of multidimensional diffusions.​

Affine Diffusions and Related Processes: Simulation, Theory and Applications

Aurélien Alfonsi
Affine Diffusions and Related Processes Simulation Theory and Applications Book PDF

Author : Aurélien Alfonsi
Publisher : Springer
Page : 264 pages
File Size : 50,8 Mb
Release : 2015-04-30
Category : Mathematics
ISBN : 9783319052212

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Affine Diffusions and Related Processes: Simulation, Theory and Applications by Aurélien Alfonsi Pdf

This book gives an overview of affine diffusions, from Ornstein-Uhlenbeck processes to Wishart processes and it considers some related diffusions such as Wright-Fisher processes. It focuses on different simulation schemes for these processes, especially second-order schemes for the weak error. It also presents some models, mostly in the field of finance, where these methods are relevant and provides some numerical experiments. The book explains the mathematical background to understand affine diffusions and analyze the accuracy of the schemes.

Monte Carlo and Quasi-Monte Carlo Methods

Art B. Owen,Peter W. Glynn
Monte Carlo and Quasi Monte Carlo Methods Book PDF

Author : Art B. Owen,Peter W. Glynn
Publisher : Springer
Page : 479 pages
File Size : 40,9 Mb
Release : 2018-07-03
Category : Computers
ISBN : 9783319914367

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Monte Carlo and Quasi-Monte Carlo Methods by Art B. Owen,Peter W. Glynn Pdf

This book presents the refereed proceedings of the Twelfth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at Stanford University (California) in August 2016. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising in particular, in finance, statistics, computer graphics and the solution of PDEs.

Geometry and Invariance in Stochastic Dynamics

Stefania Ugolini,Marco Fuhrman,Elisa Mastrogiacomo,Paola Morando,Barbara Rüdiger
Geometry and Invariance in Stochastic Dynamics Book PDF

Author : Stefania Ugolini,Marco Fuhrman,Elisa Mastrogiacomo,Paola Morando,Barbara Rüdiger
Publisher : Springer Nature
Page : 273 pages
File Size : 46,5 Mb
Release : 2022-02-09
Category : Mathematics
ISBN : 9783030874322

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Geometry and Invariance in Stochastic Dynamics by Stefania Ugolini,Marco Fuhrman,Elisa Mastrogiacomo,Paola Morando,Barbara Rüdiger Pdf

This book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications. The purpose of the present book is to present the state of the art of the studies on stochastic systems from this point of view, present some of the underlying fundamental ideas and methods involved, and to outline the main lines for future developments. The main focus is on bridging the gap between deterministic and stochastic approaches, with the goal of contributing to the elaboration of a unified theory that will have a great impact both from the theoretical point of view and the point of view of applications. The reader is a mathematician or a theoretical physicist. The main discipline is stochastic analysis with profound ideas coming from Mathematical Physics and Lie’s Group Geometry. While the audience consists essentially of academicians, the reader can also be a practitioner with Ph.D., who is interested in efficient stochastic modelling.

Mathematical Modelling and Numerical Methods in Finance

Alain Bensoussan,Qiang Zhang
Mathematical Modelling and Numerical Methods in Finance Book PDF

Author : Alain Bensoussan,Qiang Zhang
Publisher : Elsevier
Page : 743 pages
File Size : 44,9 Mb
Release : 2009-06-16
Category : Mathematics
ISBN : 9780080931005

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Mathematical Modelling and Numerical Methods in Finance by Alain Bensoussan,Qiang Zhang Pdf

Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains. Coverage of all aspects of quantitative finance including models, computational methods and applications Provides an overview of new ideas and results Contributors are leaders of the field

Stochastic Calculus of Variations in Mathematical Finance

Paul Malliavin,Anton Thalmaier
Stochastic Calculus of Variations in Mathematical Finance Book PDF

Author : Paul Malliavin,Anton Thalmaier
Publisher : Springer Science & Business Media
Page : 148 pages
File Size : 52,7 Mb
Release : 2006-02-25
Category : Business & Economics
ISBN : 9783540307990

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Stochastic Calculus of Variations in Mathematical Finance by Paul Malliavin,Anton Thalmaier Pdf

Highly esteemed author Topics covered are relevant and timely

Stochastic Analysis and Applications to Finance

Tusheng Zhang
Stochastic Analysis and Applications to Finance Book PDF

Author : Tusheng Zhang
Publisher : World Scientific
Page : 465 pages
File Size : 54,8 Mb
Release : 2012
Category : Business & Economics
ISBN : 9789814383585

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Stochastic Analysis and Applications to Finance by Tusheng Zhang Pdf

This volume is a collection of solicited and refereed articles from distinguished researchers across the field of stochastic analysis and its application to finance. The articles represent new directions and newest developments in this exciting and fast growing area. The covered topics range from Markov processes, backward stochastic differential equations, stochastic partial differential equations, stochastic control, potential theory, functional inequalities, optimal stopping, portfolio selection, to risk measure and risk theory. It will be a very useful book for young researchers who want to learn about the research directions in the area, as well as experienced researchers who want to know about the latest developments in the area of stochastic analysis and mathematical finance. Sample Chapter(s). Editorial Foreword (58 KB). Chapter 1: Non-Linear Evolution Equations Driven by Rough Paths (399 KB). Contents: Non-Linear Evolution Equations Driven by Rough Paths (Thomas Cass, Zhongmin Qian and Jan Tudor); Optimal Stopping Times with Different Information Levels and with Time Uncertainty (Arijit Chakrabarty and Xin Guo); Finite Horizon Optimal Investment and Consumption with CARA Utility and Proportional Transaction Costs (Yingshan Chen, Min Dai and Kun Zhao); MUniform Integrability of Exponential Martingales and Spectral Bounds of Non-Local Feynman-Kac Semigroups (Zhen-Qing Chen); Continuous-Time Mean-Variance Portfolio Selection with Finite Transactions (Xiangyu Cui, Jianjun Gao and Duan Li); Quantifying Model Uncertainties in the Space of Probability Measures (J Duan, T Gao and G He); A PDE Approach to Multivariate Risk Theory (Robert J Elliott, Tak Kuen Siu and Hailiang Yang); Stochastic Analysis on Loop Groups (Shizan Fang); Existence and Stability of Measure Solutions for BSDE with Generators of Quadratic Growth (Alexander Fromm, Peter Imkeller and Jianing Zhang); Convex Capital Requirements for Large Portfolios (Hans FAllmer and Thomas Knispel); The Mixed Equilibrium of Insider Trading in the Market with Rational Expected Price (Fuzhou Gong and Hong Liu); Some Results on Backward Stochastic Differential Equations Driven by Fractional Brownian Motions (Yaozhong Hu, Daniel Ocone and Jian Song); Potential Theory of Subordinate Brownian Motions Revisited (Panki Kim, Renming Song and Zoran Vondraiek); Research on Social Causes of the Financial Crisis (Steven Kou); Wick Formulas and Inequalities for the Quaternion Gaussian and -Permanental Variables (Wenbo V Li and Ang Wei); Further Study on Web Markov Skeleton Processes (Yuting Liu, Zhi-Ming Ma and Chuan Zhou); MLE of Parameters in the Drifted Brownian Motion and Its Error (Lemee Nakamura and Weian Zheng); Optimal Partial Information Control of SPDEs with Delay and Time-Advanced Backward SPDEs (Bernt yksendal, Agn s Sulem and Tusheng Zhang); Simulation of Diversified Portfolios in Continuous Financial Markets (Eckhard Platen and Renata Rendek); Coupling and Applications (Feng-Yu Wang); SDEs and a Generalised Burgers Equation (Jiang-Lun Wu and Wei Yang); Mean-Variance Hedging in the Discontinuous Case (Jianming Xia). Readership: Graduates and researchers in stochatic analysis and mathematical finance.

Discrete-Time Semi-Markov Random Evolutions and Their Applications

Nikolaos Limnios,Anatoliy Swishchuk
Discrete Time Semi Markov Random Evolutions and Their Applications Book PDF

Author : Nikolaos Limnios,Anatoliy Swishchuk
Publisher : Springer Nature
Page : 206 pages
File Size : 48,6 Mb
Release : 2023-07-24
Category : Mathematics
ISBN : 9783031334290

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Discrete-Time Semi-Markov Random Evolutions and Their Applications by Nikolaos Limnios,Anatoliy Swishchuk Pdf

This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak convergence results in the series scheme, and their extensions in some additional directions, including reduced random media, controlled processes, and optimal stopping. Finally, applications of discrete-time semi-Markov random evolutions in epidemiology and financial mathematics are discussed. This book will be of interest to researchers and graduate students in applied mathematics and statistics, and other disciplines, including engineering, epidemiology, finance and economics, who are concerned with stochastic models of systems.

Handbook of Financial Econometrics

Yacine Ait-Sahalia,Lars Peter Hansen
Handbook of Financial Econometrics Book PDF

Author : Yacine Ait-Sahalia,Lars Peter Hansen
Publisher : Elsevier
Page : 808 pages
File Size : 54,6 Mb
Release : 2009-10-19
Category : Business & Economics
ISBN : 0080929842

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Handbook of Financial Econometrics by Yacine Ait-Sahalia,Lars Peter Hansen Pdf

This collection of original articles—8 years in the making—shines a bright light on recent advances in financial econometrics. From a survey of mathematical and statistical tools for understanding nonlinear Markov processes to an exploration of the time-series evolution of the risk-return tradeoff for stock market investment, noted scholars Yacine Aït-Sahalia and Lars Peter Hansen benchmark the current state of knowledge while contributors build a framework for its growth. Whether in the presence of statistical uncertainty or the proven advantages and limitations of value at risk models, readers will discover that they can set few constraints on the value of this long-awaited volume. Presents a broad survey of current research—from local characterizations of the Markov process dynamics to financial market trading activity Contributors include Nobel Laureate Robert Engle and leading econometricians Offers a clarity of method and explanation unavailable in other financial econometrics collections

Marginal and Functional Quantization of Stochastic Processes

Harald Luschgy,Gilles Pagès
Marginal and Functional Quantization of Stochastic Processes Book PDF

Author : Harald Luschgy,Gilles Pagès
Publisher : Springer Nature
Page : 918 pages
File Size : 46,9 Mb
Release : 2023-12-06
Category : Mathematics
ISBN : 9783031454646

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Marginal and Functional Quantization of Stochastic Processes by Harald Luschgy,Gilles Pagès Pdf

Vector Quantization, a pioneering discretization method based on nearest neighbor search, emerged in the 1950s primarily in signal processing, electrical engineering, and information theory. Later in the 1960s, it evolved into an automatic classification technique for generating prototypes of extensive datasets. In modern terms, it can be recognized as a seminal contribution to unsupervised learning through the k-means clustering algorithm in data science. In contrast, Functional Quantization, a more recent area of study dating back to the early 2000s, focuses on the quantization of continuous-time stochastic processes viewed as random vectors in Banach function spaces. This book distinguishes itself by delving into the quantization of random vectors with values in a Banach space—a unique feature of its content. Its main objectives are twofold: first, to offer a comprehensive and cohesive overview of the latest developments as well as several new results in optimal quantization theory, spanning both finite and infinite dimensions, building upon the advancements detailed in Graf and Luschgy's Lecture Notes volume. Secondly, it serves to demonstrate how optimal quantization can be employed as a space discretization method within probability theory and numerical probability, particularly in fields like quantitative finance. The main applications to numerical probability are the controlled approximation of regular and conditional expectations by quantization-based cubature formulas, with applications to time-space discretization of Markov processes, typically Brownian diffusions, by quantization trees. While primarily catering to mathematicians specializing in probability theory and numerical probability, this monograph also holds relevance for data scientists, electrical engineers involved in data transmission, and professionals in economics and logistics who are intrigued by optimal allocation problems.

Financial Instrument Pricing Using C++

Daniel J. Duffy
Financial Instrument Pricing Using C Book PDF

Author : Daniel J. Duffy
Publisher : John Wiley & Sons
Page : 1168 pages
File Size : 53,6 Mb
Release : 2018-09-05
Category : Business & Economics
ISBN : 9781119170495

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Financial Instrument Pricing Using C++ by Daniel J. Duffy Pdf

An integrated guide to C++ and computational finance This complete guide to C++ and computational finance is a follow-up and major extension to Daniel J. Duffy's 2004 edition of Financial Instrument Pricing Using C++. Both C++ and computational finance have evolved and changed dramatically in the last ten years and this book documents these improvements. Duffy focuses on these developments and the advantages for the quant developer by: Delving into a detailed account of the new C++11 standard and its applicability to computational finance. Using de-facto standard libraries, such as Boost and Eigen to improve developer productivity. Developing multiparadigm software using the object-oriented, generic, and functional programming styles. Designing flexible numerical algorithms: modern numerical methods and multiparadigm design patterns. Providing a detailed explanation of the Finite Difference Methods through six chapters, including new developments such as ADE, Method of Lines (MOL), and Uncertain Volatility Models. Developing applications, from financial model to algorithmic design and code, through a coherent approach. Generating interoperability with Excel add-ins, C#, and C++/CLI. Using random number generation in C++11 and Monte Carlo simulation. Duffy adopted a spiral model approach while writing each chapter of Financial Instrument Pricing Using C++ 2e: analyse a little, design a little, and code a little. Each cycle ends with a working prototype in C++ and shows how a given algorithm or numerical method works. Additionally, each chapter contains non-trivial exercises and projects that discuss improvements and extensions to the material. This book is for designers and application developers in computational finance, and assumes the reader has some fundamental experience of C++ and derivatives pricing. HOW TO RECEIVE THE SOURCE CODE Once you have purchased a copy of the book please send an email to the author dduffyATdatasim.nl requesting your personal and non-transferable copy of the source code. Proof of purchase is needed. The subject of the mail should be “C++ Book Source Code Request”. You will receive a reply with a zip file attachment.

Numerical Solution of Stochastic Differential Equations with Jumps in Finance

Eckhard Platen,Nicola Bruti-Liberati
Numerical Solution of Stochastic Differential Equations with Jumps in Finance Book PDF

Author : Eckhard Platen,Nicola Bruti-Liberati
Publisher : Springer Science & Business Media
Page : 868 pages
File Size : 54,5 Mb
Release : 2010-07-23
Category : Mathematics
ISBN : 9783642136948

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Numerical Solution of Stochastic Differential Equations with Jumps in Finance by Eckhard Platen,Nicola Bruti-Liberati Pdf

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.

Simulation and Inference for Stochastic Differential Equations

Stefano M. Iacus
Simulation and Inference for Stochastic Differential Equations Book PDF

Author : Stefano M. Iacus
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 50,7 Mb
Release : 2009-04-27
Category : Computers
ISBN : 9780387758398

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Simulation and Inference for Stochastic Differential Equations by Stefano M. Iacus Pdf

This book covers a highly relevant and timely topic that is of wide interest, especially in finance, engineering and computational biology. The introductory material on simulation and stochastic differential equation is very accessible and will prove popular with many readers. While there are several recent texts available that cover stochastic differential equations, the concentration here on inference makes this book stand out. No other direct competitors are known to date. With an emphasis on the practical implementation of the simulation and estimation methods presented, the text will be useful to practitioners and students with minimal mathematical background. What’s more, because of the many R programs, the information here is appropriate for many mathematically well educated practitioners, too.

Numerical Methods in Computational Finance

Daniel J. Duffy
Numerical Methods in Computational Finance Book PDF

Author : Daniel J. Duffy
Publisher : John Wiley & Sons
Page : 551 pages
File Size : 48,8 Mb
Release : 2022-03-14
Category : Business & Economics
ISBN : 9781119719724

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Numerical Methods in Computational Finance by Daniel J. Duffy Pdf

This book is a detailed and step-by-step introduction to the mathematical foundations of ordinary and partial differential equations, their approximation by the finite difference method and applications to computational finance. The book is structured so that it can be read by beginners, novices and expert users. Part A Mathematical Foundation for One-Factor Problems Chapters 1 to 7 introduce the mathematical and numerical analysis concepts that are needed to understand the finite difference method and its application to computational finance. Part B Mathematical Foundation for Two-Factor Problems Chapters 8 to 13 discuss a number of rigorous mathematical techniques relating to elliptic and parabolic partial differential equations in two space variables. In particular, we develop strategies to preprocess and modify a PDE before we approximate it by the finite difference method, thus avoiding ad-hoc and heuristic tricks. Part C The Foundations of the Finite Difference Method (FDM) Chapters 14 to 17 introduce the mathematical background to the finite difference method for initial boundary value problems for parabolic PDEs. It encapsulates all the background information to construct stable and accurate finite difference schemes. Part D Advanced Finite Difference Schemes for Two-Factor Problems Chapters 18 to 22 introduce a number of modern finite difference methods to approximate the solution of two factor partial differential equations. This is the only book we know of that discusses these methods in any detail. Part E Test Cases in Computational Finance Chapters 23 to 26 are concerned with applications based on previous chapters. We discuss finite difference schemes for a wide range of one-factor and two-factor problems. This book is suitable as an entry-level introduction as well as a detailed treatment of modern methods as used by industry quants and MSc/MFE students in finance. The topics have applications to numerical analysis, science and engineering. More on computational finance and the author’s online courses, see www.datasim.nl.

Stochastic Analysis, Stochastic Systems, and Applications to Finance

Allanus Hak-Man Tsoi,David Nualart,George Yin
Stochastic Analysis Stochastic Systems and Applications to Finance Book PDF

Author : Allanus Hak-Man Tsoi,David Nualart,George Yin
Publisher : World Scientific
Page : 274 pages
File Size : 49,6 Mb
Release : 2011
Category : Business & Economics
ISBN : 9789814355711

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Stochastic Analysis, Stochastic Systems, and Applications to Finance by Allanus Hak-Man Tsoi,David Nualart,George Yin Pdf

Pt. I. Stochastic analysis and systems. 1. Multidimensional Wick-Ito formula for Gaussian processes / D. Nualart and S. Ortiz-Latorre. 2. Fractional white noise multiplication / A.H. Tsoi. 3. Invariance principle of regime-switching diffusions / C. Zhu and G. Yin -- pt. II. Finance and stochastics. 4. Real options and competition / A. Bensoussan, J.D. Diltz and S.R. Hoe. 5. Finding expectations of monotone functions of binary random variables by simulation, with applications to reliability, finance, and round robin tournaments / M. Brown, E.A. Pekoz and S.M. Ross. 6. Filtering with counting process observations and other factors : applications to bond price tick data / X. Hu, D.R. Kuipers and Y. Zeng. 7. Jump bond markets some steps towards general models in applications to hedging and utility problems / M. Kohlmann and D. Xiong. 8. Recombining tree for regime-switching model : algorithm and weak convergence / R.H. Liu. 9. Optimal reinsurance under a jump diffusion model / S. Luo. 10. Applications of counting processes and martingales in survival analysis / J. Sun. 11. Stochastic algorithms and numerics for mean-reverting asset trading / Q. Zhang, C. Zhuang and G. Yin