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An Introduction to Continuous-Time Stochastic Processes by Vincenzo Capasso,David Bakstein Pdf
This concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. Balancing theory and applications, the authors use stochastic methods and concrete examples to model real-world problems from engineering, biomathematics, biotechnology, and finance. Suitable as a textbook for graduate or advanced undergraduate courses, the work may also be used for self-study or as a reference. The book will be of interest to students, pure and applied mathematicians, and researchers or practitioners in mathematical finance, biomathematics, physics, and engineering.
Continuous Time Processes for Finance by Donatien Hainaut Pdf
This book explores recent topics in quantitative finance with an emphasis on applications and calibration to time-series. This last aspect is often neglected in the existing mathematical finance literature while it is crucial for risk management. The first part of this book focuses on switching regime processes that allow to model economic cycles in financial markets. After a presentation of their mathematical features and applications to stocks and interest rates, the estimation with the Hamilton filter and Markov Chain Monte-Carlo algorithm (MCMC) is detailed. A second part focuses on self-excited processes for modeling the clustering of shocks in financial markets. These processes recently receive a lot of attention from researchers and we focus here on its econometric estimation and its simulation. A chapter is dedicated to estimation of stochastic volatility models. Two chapters are dedicated to the fractional Brownian motion and Gaussian fields. After a summary of their features, we present applications for stock and interest rate modeling. Two chapters focuses on sub-diffusions that allows to replicate illiquidity in financial markets. This book targets undergraduate students who have followed a first course of stochastic finance and practitioners as quantitative analyst or actuaries working in risk management.
An Introduction to Continuous-Time Stochastic Processes by Vincenzo Capasso,David Bakstein Pdf
Expanding on the first edition of An Introduction to Continuous-Time Stochastic Processes, this concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. A balance of theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required.
Continuous-time Stochastic Control and Optimization with Financial Applications by Huyên Pham Pdf
Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.
Stochastic Calculus for Finance I by Steven Shreve Pdf
Developed for the professional Master's program in Computational Finance at Carnegie Mellon, the leading financial engineering program in the U.S. Has been tested in the classroom and revised over a period of several years Exercises conclude every chapter; some of these extend the theory while others are drawn from practical problems in quantitative finance
Financial Markets in Continuous Time by Rose-Anne Dana,Monique Jeanblanc-Picqué,Monique Jeanblanc Pdf
This book explains key financial concepts, mathematical tools and theories of mathematical finance. It is organized in four parts. The first brings together a number of results from discrete-time models. The second develops stochastic continuous-time models for the valuation of financial assets (the Black-Scholes formula and its extensions), for optimal portfolio and consumption choice, and for obtaining the yield curve and pricing interest rate products. The third part recalls some concepts and results of equilibrium theory and applies this in financial markets. The last part tackles market incompleteness and the valuation of exotic options.
Robert C. Merton's widely-used text provides an overview and synthesis of finance theory from the perspective of continuous-time analysis. It covers individual finance choice, corporate finance, financial intermediation, capital markets, and selected topics on the interface between private and public finance.
Financial Markets in Continuous Time by Rose-Anne Dana,Monique Jeanblanc Pdf
This book explains key financial concepts, mathematical tools and theories of mathematical finance. It is organized in four parts. The first brings together a number of results from discrete-time models. The second develops stochastic continuous-time models for the valuation of financial assets (the Black-Scholes formula and its extensions), for optimal portfolio and consumption choice, and for obtaining the yield curve and pricing interest rate products. The third part recalls some concepts and results of equilibrium theory and applies this in financial markets. The last part tackles market incompleteness and the valuation of exotic options.
Discrete Time Series, Processes, and Applications in Finance by Gilles Zumbach Pdf
Most financial and investment decisions are based on considerations of possible future changes and require forecasts on the evolution of the financial world. Time series and processes are the natural tools for describing the dynamic behavior of financial data, leading to the required forecasts. This book presents a survey of the empirical properties of financial time series, their descriptions by means of mathematical processes, and some implications for important financial applications used in many areas like risk evaluation, option pricing or portfolio construction. The statistical tools used to extract information from raw data are introduced. Extensive multiscale empirical statistics provide a solid benchmark of stylized facts (heteroskedasticity, long memory, fat-tails, leverage...), in order to assess various mathematical structures that can capture the observed regularities. The author introduces a broad range of processes and evaluates them systematically against the benchmark, summarizing the successes and limitations of these models from an empirical point of view. The outcome is that only multiscale ARCH processes with long memory, discrete multiplicative structures and non-normal innovations are able to capture correctly the empirical properties. In particular, only a discrete time series framework allows to capture all the stylized facts in a process, whereas the stochastic calculus used in the continuum limit is too constraining. The present volume offers various applications and extensions for this class of processes including high-frequency volatility estimators, market risk evaluation, covariance estimation and multivariate extensions of the processes. The book discusses many practical implications and is addressed to practitioners and quants in the financial industry, as well as to academics, including graduate (Master or PhD level) students. The prerequisites are basic statistics and some elementary financial mathematics.
Continuous-Time Models in Corporate Finance, Banking, and Insurance by Santiago Moreno-Bromberg,Jean-Charles Rochet Pdf
Continuous-Time Models in Corporate Finance synthesizes four decades of research to show how stochastic calculus can be used in corporate finance. Combining mathematical rigor with economic intuition, Santiago Moreno-Bromberg and Jean-Charles Rochet analyze corporate decisions such as dividend distribution, the issuance of securities, and capital structure and default. They pay particular attention to financial intermediaries, including banks and insurance companies. The authors begin by recalling the ways that option-pricing techniques can be employed for the pricing of corporate debt and equity. They then present the dynamic model of the trade-off between taxes and bankruptcy costs and derive implications for optimal capital structure. The core chapter introduces the workhorse liquidity-management model—where liquidity and risk management decisions are made in order to minimize the costs of external finance. This model is used to study corporate finance decisions and specific features of banks and insurance companies. The book concludes by presenting the dynamic agency model, where financial frictions stem from the lack of interest alignment between a firm's manager and its financiers. The appendix contains an overview of the main mathematical tools used throughout the book. Requiring some familiarity with stochastic calculus methods, Continuous-Time Models in Corporate Finance will be useful for students, researchers, and professionals who want to develop dynamic models of firms' financial decisions.
Handbook of Financial Time Series by Torben Gustav Andersen,Richard A. Davis,Jens-Peter Kreiß,Thomas V. Mikosch Pdf
The Handbook of Financial Time Series gives an up-to-date overview of the field and covers all relevant topics both from a statistical and an econometrical point of view. There are many fine contributions, and a preamble by Nobel Prize winner Robert F. Engle.
Stochastic Processes with Applications to Finance by Masaaki Kijima Pdf
In recent years, modeling financial uncertainty using stochastic processes has become increasingly important, but it is commonly perceived as requiring a deep mathematical background. Stochastic Processes with Applications to Finance shows that this is not necessarily so. It presents the theory of discrete stochastic processes and their applications in finance in an accessible treatment that strikes a balance between the abstract and the practical. Using an approach that views sophisticated stochastic calculus as based on a simple class of discrete processes-"random walks"-the author first provides an elementary introduction to the relevant areas of real analysis and probability. He then uses random walks to explain the change of measure formula, the reflection principle, and the Kolmogorov backward equation. The Black-Scholes formula is derived as a limit of binomial model, and applications to the pricing of derivative securities are presented. Another primary focus of the book is the pricing of corporate bonds and credit derivatives, which the author explains in terms of discrete default models. By presenting important results in discrete processes and showing how to transfer those results to their continuous counterparts, Stochastic Processes with Applications to Finance imparts an intuitive and practical understanding of the subject. This unique treatment is ideal both as a text for a graduate-level class and as a reference for researchers and practitioners in financial engineering, operations research, and mathematical and statistical finance.
Stochastic Processes in Science, Engineering and Finance by Frank Beichelt Pdf
This book presents a self-contained introduction to stochastic processes with emphasis on their applications in science, engineering, finance, computer science, and operations research. It provides theoretical foundations for modeling time-dependent random phenomena in these areas and illustrates their application by analyzing numerous practical examples. The treatment assumes few prerequisites, requiring only the standard mathematical maturity acquired by undergraduate applied science students. It includes an introductory chapter that summarizes the basic probability theory needed as background. Numerous exercises reinforce the concepts and techniques discussed and allow readers to assess their grasp of the subject. Solutions to most of the exercises are provided in an appendix. While focused primarily on practical aspects, the presentation includes some important proofs along with more challenging examples and exercises for those more theoretically inclined. Mastering the contents of this book prepares readers to apply stochastic modeling in their own fields and enables them to work more creatively with software designed for dealing with the data analysis aspects of stochastic processes.