Series In Quantitative Finance – serie

Each financial crisis calls for — by its novelty and the mechanisms it shares with preceding crises — appropriate means to analyze financial risks. In Extreme Financial Risks and Asset Allocation, the authors present in an accessible and timely manner the concepts, methods, and techniques that are essential for an understanding of these risks in an environment where asset prices are subject to sudden, rough, and unpredictable changes. These phenomena, mathematically known as “jumps”, play an important role in practice. Their quantitative treatment is generally tricky and is sparsely tackled in similar books. One of the main appeals of this book lies in its approachable and concise presentation of the ad hoc mathematical tools without sacrificing the necessary rigor and precision.This book contains theories and methods which are usually found in highly technical mathematics books or in scattered, often very recent, research articles. It is a remarkable pedagogical work that makes these difficult results accessible to a large readership. Researchers, Masters and PhD students, and financial engineers alike will find this book highly useful.

Although there are several publications on similar subjects, this book mainly focuses on pricing of options and bridges the gap between Mathematical Finance and Numerical Methodologies. The author collects the key contributions of several monographs and selected literature, values and displays their importance, and composes them here to create a work which has its own characteristics in content and style.This invaluable book provides working Matlab codes not only to implement the algorithms presented in the text, but also to help readers code their own pricing algorithms in their preferred programming languages. Availability of the codes under an Internet site is also offered by the author.Not only does this book serve as a textbook in related undergraduate or graduate courses, but it can also be used by those who wish to implement or learn pricing algorithms by themselves. The basic methods of option pricing are presented in a self-contained and unified manner, and will hopefully help readers improve their mathematical and computational backgrounds for more advanced topics.Errata(s)Errata

This volume offers the reader practical methods to compute the option prices in the incomplete asset markets. The [GLP & MEMM] pricing models are clearly introduced, and the properties of these models are discussed in great detail. It is shown that the geometric Lévy process (GLP) is a typical example of the incomplete market, and that the MEMM (minimal entropy martingale measure) is an extremely powerful pricing measure.This volume also presents the calibration procedure of the [GLP & MEMM] model that has been widely used in the application of practical problems.

This book provides a broad introduction of modern asset pricing theory with equal treatments for both discrete-time and continuous-time modeling. Both the no-arbitrage and the general equilibrium approaches of asset pricing theory are treated coherently within the general equilibrium framework.The analyses and coverage are up to date, comprehensive and in-depth. Topics include microeconomic foundation of asset pricing theory, the no-arbitrage principle and fundamental theorem, risk measurement and risk management, sequential portfolio choice, equity premium decomposition, option pricing, bond pricing and term structure of interest rates. The merits and limitations are expounded with respect to allocation and information market efficiency, along with the classical expectations hypothesis concerning the information content of yield curve and bond prices. Efforts are also made towards the resolution of several well-documented puzzles in empirical finance, which include the equity premium puzzle, the risk free rate puzzle, and the money-ness bias phenomenon of Black-Scholes option pricing model.The theory is self-contained and unified in presentation. The inclusion of proofs and derivations to enhance the transparency of the underlying arguments and conditions for the validity of the economic theory makes an ideal advanced textbook or reference book for graduate students specializing in financial economics and quantitative finance. The explanations are detailed enough to capture the interest of those curious readers, and complete enough to provide necessary background material needed to explore further the subject and research literature.

This book provides the reader with a background on simulating copulas and multivariate distributions in general. It unifies the scattered literature on the simulation of various families of copulas (elliptical, Archimedean, Marshall-Olkin type, etc.) as well as on different construction principles (factor models, pair-copula construction, etc.). The book is self-contained and unified in presentation and can be used as a textbook for advanced undergraduate or graduate students with a firm background in stochastics. Alongside the theoretical foundation, ready-to-implement algorithms and many examples make this book a valuable tool for anyone who is applying the methodology.

This book presents some new models and methods in the context of dynamical portfolio optimization. It encapsulates the authors' recent progress in their research on several interesting, featured issues of dynamic portfolio optimization problems with default contagion, tracking benchmark, consumption habit, and reinforcement learning.These models include the default contagion model with infinite regime-switching under complete information and partial information; portfolio optimization model with consumption habit formation; optimal tracking model; extended Merton's problem with relaxed benchmark tracking and reinforcement learning of tracking portfolio.The methods for addressing these problems are by developing the monotone dynamical system, martingale representation theorem under partial information, quadratic BSDE with jumps, duality method, decomposition-homogenization technique of Neumann problem, stochastic flow, and q-function learning with state reflection.For the sake of the reader's convenience, preliminary knowledge on stochastic analysis and stochastic control are summarized in Chapters 2 and 3, which also serve as a brief basic introduction to the theory of SDEs, BSDEs, and the theory of optimal stochastic control.The book will be a good reference for graduate students and researchers working on stochastic control and mathematical finance. The reader may pursue some presented research problems and be inspired to formulate and study other new and interesting problems in dynamic portfolio optimization and beyond.