Springer Series in Operations Research and Financial Engineering

Mathematical Risk Analysis

Dependence, Risk Bounds, Optimal Allocations and Portfolios

Authors: Rüschendorf, Ludger

  • Up-to-date treatment of the main concepts and techniques used in mathematical risk analysis
  • Clearly structured guide  
  • Gives orientation and help to acquire a solid fundament for working in this area​  
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About this book

The author's particular interest in the area of risk measures is to combine this theory with the analysis of dependence properties. The present volume gives an introduction of basic concepts and methods in mathematical risk analysis, in particular of those parts of risk theory that are of special relevance to finance and insurance. Describing the influence of dependence in multivariate stochastic models on risk vectors is the main focus of the text that presents main ideas and methods as well as their relevance to practical applications.   The first part introduces basic probabilistic tools and methods of distributional analysis, and describes their use to the modeling of dependence and to the derivation of risk bounds in these models. In the second, part risk measures with a particular focus on those in the financial and insurance context are presented. The final parts are then devoted to applications relevant to optimal risk allocation, optimal portfolio problems as well as to the optimization of insurance contracts. Good knowledge of basic probability and statistics as well as of basic general mathematics is a prerequisite for comfortably reading and working with the present volume, which is intended for graduate students, practitioners and researchers and can serve as a reference resource for the main concepts and techniques.      

About the authors

Ludger Rüschendorf, Professor of Mathematical Stochastics, studied Mathematics, Physics and Economics in Münster. Diploma thesis 1972 - PhD 1974 in Hamburg in Asymptotic Statistics - Habilitation thesis 1979 in Aachen in the area of stochastic ordering, masstransportation and Fréchet bounds - Professorships in Germany: 1981-1987 in Freiburg, 1987-1993 in Münster, 1993- in Freiburg.  He is elected member of the ISI, and author and co-author of several books and about 180 research papers.

Reviews

From the reviews:

“The book contains four parts: stochastic dependence and extremal risk, risk measures and worst case portfolios, optimal risk allocation, and optimal portfolios and extreme risk. … the book will be definitely interesting to researchers and graduate students in the areas of insurance, financial mathematics, risk management, etc., as it gives a clear picture which research directions have been pursued and to what extent.” (Jonas Šiaulys, zbMATH, Vol. 1266, 2013)

Table of contents (14 chapters)

  • Copulas, Sklar’s Theorem, and Distributional Transform

    Rüschendorf, Ludger

    Pages 3-34

  • Fréchet Classes, Risk Bounds, and Duality Theory

    Rüschendorf, Ludger

    Pages 35-51

  • Convex Order, Excess of Loss, and Comonotonicity

    Rüschendorf, Ludger

    Pages 53-70

  • Bounds for the Distribution Function and Value at Risk of the Joint Portfolio

    Rüschendorf, Ludger

    Pages 71-90

  • Restrictions on the Dependence Structure

    Rüschendorf, Ludger

    Pages 91-112

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-642-33590-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-642-33589-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-3-642-43016-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Risk Analysis
Book Subtitle
Dependence, Risk Bounds, Optimal Allocations and Portfolios
Authors
Series Title
Springer Series in Operations Research and Financial Engineering
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-33590-7
DOI
10.1007/978-3-642-33590-7
Hardcover ISBN
978-3-642-33589-1
Softcover ISBN
978-3-642-43016-9
Series ISSN
1431-8598
Edition Number
1
Number of Pages
XII, 408
Topics