Stochastic Drawdowns

Stochastic Drawdowns consists of some recent advances on Hongzhong Zhang's own quantitative research of the well-known risk measures, drawdowns and maximum drawdowns. In particular, the author provides an extensive probabilistic study of several quantities related to drawdowns, which include the dra [...]
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Stochastic Drawdowns consists of some recent advances on Hongzhong Zhang's own quantitative research of the well-known risk measures, drawdowns and maximum drawdowns. In particular, the author provides an extensive probabilistic study of several quantities related to drawdowns, which include the drawdown risk in finite time-horizons, the speed of market crashes (drawdowns), the occupation time (time in distress), and the duration of drawdowns. These topics can be considered as problems in advanced applied stochastic processes, and insurance/financial mathematics.Apart from the aforementioned mathematical content, the book also offers some applications of drawdowns in financial risk management and insurance. A sample of examples includes schemes on hedging and synthesizing of maximum drawdown insurances, (cancelable) drawdown swap contracts and their earlier exercising premium, as well as optimal trading and earlier liquidation premium under drawdown-type constraints such as trailing stops. This book also discusses the applications of drawdowns in detecting abrupt changes in drift of a price process.It is the goal of this book to fill the gap between theory and practice on drawdowns.On one hand, the book enables 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 tractable quantities related to drawdown risk, and a better understanding of optimal trading and execution amid challenges and risks.