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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
-->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. -->Contents: IntroductionDrawdown Measures:Drawdowns Preceding Drawups in a Finite Time-HorizonDrawdowns and the Speed of Market CrashesFrequency of Drawdowns in a Brownian Motion ModelOccupation Times Related to DrawdownsDuration of Drawdowns under Lévy ModelsApplications of Drawdown:Maximum Drawdown Insurance Using OptionsFair Premiums of Drawdown InsurancesOptimal Trading with a Trailing StopAppendix: Briefly on One-Dimensional Linear Diffusions --> -->Readership: Senior undergraduate and graduate students equipped with the knowledge of stochastic processes and financial practitioners who are interested in optimal trading and execution. -->Keywords:Drawdown;Maximum Drawdown;Insurance;Optimal TradingReview:Key Features:The first book to touch on the advanced quantitative analysis of drawdowns in the current marketA rigorous and extensive study of drawdowns from a probabilistic point of viewAddressing of important practical problems related to drawdowns