This four-volume handbook covers important concepts and tools used in the fields of financial econometrics, mathematics, statistics, and machine learning. Econometric methods have been applied in asset pricing, corporate finance, international finance, options and futures, risk management, and in stress testing for financial institutions. This handbook discusses a variety of econometric methods, including single equation multiple regression, simultaneous equation regression, and panel data analysis, among others. It also covers statistical distributions, such as the binomial and log normal distributions, in light of their applications to portfolio theory and asset management in addition to their use in research regarding options and futures contracts.In both theory and methodology, we need to rely upon mathematics, which includes linear algebra, geometry, differential equations, Stochastic differential equation (Ito calculus), optimization, constrained optimization, and others. These forms of mathematics have been used to derive capital market line, security market line (capital asset pricing model), option pricing model, portfolio analysis, and others.In recent times, an increased importance has been given to computer technology in financial research. Different computer languages and programming techniques are important tools for empirical research in finance. Hence, simulation, machine learning, big data, and financial payments are explored in this handbook.Led by Distinguished Professor Cheng Few Lee from Rutgers University, this multi-volume work integrates theoretical, methodological, and practical issues based on his years of academic and industry experience.

An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.

This rigorous textbook introduces graduate students to the principles of econometrics and statistics with a focus on methods and applications in financial research. Financial Econometrics, Mathematics, and Statistics introduces tools and methods important for both finance and accounting that assist with asset pricing, corporate finance, options and futures, and conducting financial accounting research. Divided into four parts, the text begins with topics related to regression and financial econometrics. Subsequent sections describe time-series analyses; the role of binomial, multi-nomial, and log normal distributions in option pricing models; and the application of statistics analyses to risk management. The real-world applications and problems offer students a unique insight into such topics as heteroskedasticity, regression, simultaneous equation models, panel data analysis, time series analysis, and generalized method of moments. Written by leading academics in the quantitative finance field, allows readers to implement the principles behind financial econometrics and statistics through real-world applications and problem sets. This textbook will appeal to a less-served market of upper-undergraduate and graduate students in finance, economics, and statistics. ​

This fully updated third edition is devoted to the analysis of various Stochastic Dominance (SD) decision rules. It discusses the pros and cons of each of the alternate SD rules, the application of these rules to various research areas like statistics, agriculture, medicine, measuring income inequality and the poverty level in various countries, and of course, to investment decision-making under uncertainty. The book features changes and additions to the various chapters, and also includes two completely new chapters. One deals with asymptotic SD and the relation between FSD and the maximum geometric mean (MGM) rule (or the maximum growth portfolio). The other new chapter discusses bivariate SD rules where the individual’s utility is determined not only by his own wealth, but also by his standing relative to his peer group. Stochastic Dominance: Investment Decision Making under Uncertainty, 3rd Ed. covers the following basic issues: the SD approach, asymptotic SD rules, the mean-variance (MV) approach, as well as the non-expected utility approach. The non-expected utility approach focuses on Regret Theory (RT) and mainly on prospect theory (PT) and its modified version, cumulative prospect theory (CPT) which assumes S-shape preferences. In addition to these issues the book suggests a new stochastic dominance rule called the Markowitz stochastic dominance (MSD) rule corresponding to all reverse-S-shape preferences. It also discusses the concept of the multivariate expected utility and analyzed in more detail the bivariate expected utility case. From the reviews of the second edition: "This book is an economics book about stochastic dominance. ... is certainly a valuable reference for graduate students interested in decision making under uncertainty. It investigates and compares different approaches and presents many examples. Moreover, empirical studies and experimental results play an important role in this book, which makes it interesting to read." (Nicole Bäuerle, Mathematical Reviews, Issue 2007 d)

Futures and Options are concerned with the valuation of derivatives and their application to hedging and speculating investments. This book contains 22 chapters and is divided into five parts. Part I contains an overview including a general introduction as well as an introduction to futures, options, swaps, and valuation theories. Part II: Forwards and Futures discusses futures valuation, the futures market, hedging strategies, and various types of futures. Part III: Option Theories and Applications includes both the basic and advanced valuation of options and option strategies in addition to index and currency options. Part IV: Advanced Analyses of Options takes a look at higher level strategies used to quantitatively approach the analysis of options. Part V: Special Topics of Options and Futures covers the applications of more obscure and alternative methods in derivatives as well as the derivation of the Black-Scholes Option Pricing Model.This book applies an active interdisciplinary approach to presenting the material; in other words, three projects involving the use of real-world financial data on derivative, in addition to homework assignments, are made available for students in this book.

This volume presents state-of-the-art complementarity applications, algorithms, extensions and theory in the form of eighteen papers. These at the International Conference on Com invited papers were presented plementarity 99 (ICCP99) held in Madison, Wisconsin during June 9-12, 1999 with support from the National Science Foundation under Grant DMS-9970102. Complementarity is becoming more widely used in a variety of appli cation areas. In this volume, there are papers studying the impact of complementarity in such diverse fields as deregulation of electricity mar kets, engineering mechanics, optimal control and asset pricing. Further more, application of complementarity and optimization ideas to related problems in the burgeoning fields of machine learning and data mining are also covered in a series of three articles. In order to effectively process the complementarity problems that arise in such applications, various algorithmic, theoretical and computational extensions are covered in this volume. Nonsmooth analysis has an im portant role to play in this area as can be seen from articles using these tools to develop Newton and path following methods for constrained nonlinear systems and complementarity problems. Convergence issues are covered in the context of active set methods, global algorithms for pseudomonotone variational inequalities, successive convex relaxation and proximal point algorithms. Theoretical contributions to the connectedness of solution sets and constraint qualifications in the growing area of mathematical programs with equilibrium constraints are also presented. A relaxation approach is given for solving such problems. Finally, computational issues related to preprocessing mixed complementarity problems are addressed.

Winner of the prestigious Paul A. Samuelson Award for scholarly writing on lifelong financial security, John Cochrane's Asset Pricing now appears in a revised edition that unifies and brings the science of asset pricing up to date for advanced students and professionals. Cochrane traces the pricing of all assets back to a single idea—price equals expected discounted payoff—that captures the macro-economic risks underlying each security's value. By using a single, stochastic discount factor rather than a separate set of tricks for each asset class, Cochrane builds a unified account of modern asset pricing. He presents applications to stocks, bonds, and options. Each model—consumption based, CAPM, multifactor, term structure, and option pricing—is derived as a different specification of the discounted factor. The discount factor framework also leads to a state-space geometry for mean-variance frontiers and asset pricing models. It puts payoffs in different states of nature on the axes rather than mean and variance of return, leading to a new and conveniently linear geometrical representation of asset pricing ideas. Cochrane approaches empirical work with the Generalized Method of Moments, which studies sample average prices and discounted payoffs to determine whether price does equal expected discounted payoff. He translates between the discount factor, GMM, and state-space language and the beta, mean-variance, and regression language common in empirical work and earlier theory. The book also includes a review of recent empirical work on return predictability, value and other puzzles in the cross section, and equity premium puzzles and their resolution. Written to be a summary for academics and professionals as well as a textbook, this book condenses and advances recent scholarship in financial economics.