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Although portfolio management didn't change much during the 40 years after the seminal works of Markowitz and Sharpe, the development of risk budgeting techniques marked an important milestone in the deepening of the relationship between risk and asset management. Risk parity then became a popular financial model of investment after the global financial crisis in 2008. Today, pension funds and institutional investors are using this approach in the development of smart indexing and the redefinition of long-term investment policies. Written by a well-known expert of asset management and risk parity, Introduction to Risk Parity and Budgeting provides an up-to-date treatment of this alternative method to Markowitz optimization. It builds financial exposure to equities and commodities, considers credit risk in the management of bond portfolios, and designs long-term investment policy. The first part of the book gives a theoretical account of portfolio optimization and risk parity. The author discusses modern portfolio theory and offers a comprehensive guide to risk budgeting. Each chapter in the second part presents an application of risk parity to a specific asset class. The text covers risk-based equity indexation (also called smart beta) and shows how to use risk budgeting techniques to manage bond portfolios. It also explores alternative investments, such as commodities and hedge funds, and applies risk parity techniques to multi-asset classes. The book's first appendix provides technical materials on optimization problems, copula functions, and dynamic asset allocation. The second appendix contains 30 tutorial exercises. Solutions to the exercises, slides for instructors, and Gauss computer programs to reproduce the book's examples, tables, and figures are available on the author's website.

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中文翻译Introduction to Linear Algebra, 5th Edition 9.2节 本节的要点可由一句话表达：当你转置一个向量 z 或一个矩阵 A 时，也要取其复共轭。不要停在 z T 或 AT 。反转所有虚部的符号。从列向量 zj = aj + ibj 开始，其符合标准的行向量 z T 为分量是 aj − ibj 的共轭转置： 这里是转为 z T 的一个原因。实向量长度的平方为 x21 + · · · + x2n 。复向量长度的平方并非 z12 + · · · + zn2 。 用这个错误定义的话，(1, i) 的长度将是 12 + i2 = 0。一个非零向量将有 0 长度——不可接受。其它向 量将有复数长度。我们想要 a2 + b2 而不是 (a + bi)2 ，即绝对值的平方。就是 (a + bi) 乘以 (a − bi)。 2 对于每个分量，我们想使 zj 乘以 z j ，即 |zj | = a2j + b2j 。当 z 的分量乘以乘以 z 的分量时：

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WILEY SERIES IN MATHEMATICAL AND COMPUTATIONAL BIOLOGY Editor-in-Chief Simon Levin Department of Ecology and Evolutionary Biology, Princeton University, USA Associate Editors Zvia Agur, Tel-Aviv University, Israel Odo Diekmann, University of Utrecht, The Netherlands Marcus Feldman, Stanford University, USA Bryan Grenfell, Cambridge University, UK Philip Maini, Oxford University, UK Martin Nowak, Oxford University, UK Karl Sigmund, University of Vienna, Austria CHAPLAIN/SINGH/MCLACHLAN—On Growth and Form: Spatio-temporal Pattern Formation in Biology CHRISTIANSEN—Population Genetics of Multiple Loci CLOTE/BACKOFEN—Computational Molecular Biology: An Introduction DIEKMANN/HEESTERBEEK—Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation Reflecting the rapidly growing interest and research in the field of mathematical biology, this outstanding new book series examines the integration of mathematical and computational methods into biological work. It also encourages the advancement of theoretical and quantitative approaches to biology, and the development of biological organisation and function. The scope of the series is broad, ranging from molecular structure and processes to the dynamics of ecosystems and the biosphere, but unified through evolutionary and physical principles, and the interplay of processes across scales of biological organisation. Topics to be covered in the series include: • Cell and molecular biology • Functional morphology and physiology • Neurobiology and higher function • Immunology • Epidemiology • Ecological and evolutionary dynamics of interacting populations A fundamental research tool, the Wiley Series in Mathematical and Computational Biology provides essential and invaluable reading for biomathematicians and development biologists, as well as graduate students and researchers in mathematical biology and epidemiology.

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