MODERN TRENDS IN FINANCIAL ENGINEERING – serie

This introductory/intermediate level textbook focuses on mathematical programming and its applications. It introduces basic linear programming — the easiest form of mathematical programming with emphasis on economic interpretation of the model solution. Well-known applications of linear programming to problems in business and agriculture are presented.The text then extends into more advanced forms of mathematical programming including quadratic and integer programming. These models include the introduction of risk and uncertainty into decision-making and a class of models known as price endogenous models in which market equilibrium analyses can be modelled. Integer programming includes conditional decision-making model, machinery selection, and a class of models known as supply chain models.Supplements are provided to assist solution of the models using either GAMS or Excel, the two most widely used software packages for solution of mathematical programming models.

This introductory/intermediate level textbook focuses on mathematical programming and its applications. It introduces basic linear programming — the easiest form of mathematical programming with emphasis on economic interpretation of the model solution. Well-known applications of linear programming to problems in business and agriculture are presented.The text then extends into more advanced forms of mathematical programming including quadratic and integer programming. These models include the introduction of risk and uncertainty into decision-making and a class of models known as price endogenous models in which market equilibrium analyses can be modelled. Integer programming includes conditional decision-making model, machinery selection, and a class of models known as supply chain models.Supplements are provided to assist solution of the models using either GAMS or Excel, the two most widely used software packages for solution of mathematical programming models.

Futures play an integral role in the financial markets. Tens of millions of contracts are traded on futures exchanges around the globe every day. In recent years, futures have been incorporated into a wide array of financial securities and have become the driving force behind their price dynamics. Managed futures portfolios and commodity trading advisors (CTAs), with hundreds of billions under management, are major parts of the hedge fund industry.This book presents a unique stochastic control approach to dynamic futures trading. Multiple stochastic models are designed to capture the salient features of various market regimes and dynamics. They are useful for pricing futures contracts and building futures portfolios. The authors analyze the mathematical problems associated with futures trading problems in different market environments. A series of numerical examples are presented to illustrate the optimal trading strategies. In addition, analytic formulas and numerical methods are provided for fast implementation. The book is useful for practitioners interested in futures trading as well as graduate students and researchers in Quantitative Finance.

Multiscale Financial Data Analytics and Machine Learning offers a systematic and comprehensive study on the multiscale approach to financial data analytics and machine learning. This book covers an array of multiscale methods to discover the properties of various timescales embedded in a financial time series, including noise-assisted empirical mode decomposition methods. Important interpretable multiscale outputs from the estimation are recognized as a new set of features that can be used for machine learning. The feature selection problem for machine learning is examined in this volume.This book offers an applied quantitative approach that combines novel analytical methodologies and practical applications to a wide array of examples with real-world data. It is self-contained and organized in its presentation. The explanations of the methodologies are both accessible and detailed enough to capture the interest of the curious student or researcher. Step-by-step descriptions of the algorithms are provided for straightforward implementation.

Stochastic Drawdowns consists of some recent advances on Dr Hongzhong Zhang's own quantitative research of the well-known risk measures, drawdowns and maximum drawdowns. In this book, the author provides an extensive probabilistic study of different aspects of drawdown risks, which include the drawdown risk in finite time-horizons, the speed of market crashes (drawdowns), the frequency of drawdowns, the occupation time (time in distress), and the duration of drawdowns. Leveraging the knowledge in stochastic calculus, Lévy processes and optimal stopping, these topics can be considered as problems in advanced applied stochastic processes, and insurance/financial mathematics.The book also offers a number of applications of drawdowns in financial risk management, insurance, and algorithmic trading, including schemes on hedging and synthesizing of maximum drawdown options, (cancellable) drawdown insurance contracts and their fair premium, as well as optimal trading under drawdown-type constraints such as trailing stops.It is the goal of this book to offer a comprehensive characterization of drawdown risks and a handful of applications of drawdown in practice. On the one hand, the book enables interested students and researchers to learn the state-of-art probabilistic research on drawdowns, and explore new mathematical problems that are of practical importance to the financial industry. On the other hand, the book provides financial practitioners with access to a variety of analytically tractable measurements of drawdown risks, and the insight into hedging, optimal trading and execution amid challenges of these risks.

Employee stock options (ESOs) are an integral component of compensation in the US. In fact, almost all S&P 500 companies grant options to their top executives, and the total value accounts for almost half of the total pay for their CEOs. In view of the extensive use and significant cost of ESOs to firms, the Financial Accounting Standards Board (FASB) has mandated expensing ESOs since 2004. This gives rise to the need to create a reasonable valuation method for these options for most firms that grant ESOs to their employees. The valuation of ESOs involves a number of challenging issues, and is thus an important active research area in Accounting, Corporate Finance, and Financial Mathematics.In this exciting book, the author discusses the practical and challenging problems surrounding ESOs from a financial mathematician's perspective. This book provides a systematic overview of the contractual features of ESOs and thoughtful discussions of different valuation approaches, with emphasis on three major aspects: (i) hedging strategies; (ii) exercise timing; and (iii) valuation methodologies. In addition to addressing each of these categories, this book also highlights their connections and combined effects of the cost of ESOs to firms, as well as examines the implications to modeling and valuation approaches. The book features a unique approach that combines stochastic modeling and control techniques with option pricing theory, and provides formulas and numerical schemes for fast implementation and clear illustration.

Optimal Mean Reversion Trading: Mathematical Analysis and Practical Applications provides a systematic study to the practical problem of optimal trading in the presence of mean-reverting price dynamics. It is self-contained and organized in its presentation, and provides rigorous mathematical analysis as well as computational methods for trading ETFs, options, futures on commodities or volatility indices, and credit risk derivatives.This book offers a unique financial engineering approach that combines novel analytical methodologies and applications to a wide array of real-world examples. It extracts the mathematical problems from various trading approaches and scenarios, but also addresses the practical aspects of trading problems, such as model estimation, risk premium, risk constraints, and transaction costs. The explanations in the book are detailed enough to capture the interest of the curious student or researcher, and complete enough to give the necessary background material for further exploration into the subject and related literature.This book will be a useful tool for anyone interested in financial engineering, particularly algorithmic trading and commodity trading, and would like to understand the mathematically optimal strategies in different market environments.