Mathematical Risk Analysis

Dependence, Risk Bounds, Optimal Allocations and Portfolios

  • Ludger Rüschendorf

Table of contents

  1. Front Matter
    Pages i-xii
  2. Stochastic Dependence and Extremal Risk

    1. Front Matter
      Pages 1-2
    2. Ludger Rüschendorf
      Pages 35-51
    3. Ludger Rüschendorf
      Pages 53-70
    4. Ludger Rüschendorf
      Pages 91-112
    5. Ludger Rüschendorf
      Pages 113-136
  3. Risk Measures and Worst Case Portfolios

    1. Front Matter
      Pages 137-140
    2. Ludger Rüschendorf
      Pages 141-165
    3. Ludger Rüschendorf
      Pages 167-188
  4. Optimal Risk Allocation

    1. Front Matter
      Pages 223-225
    2. Ludger Rüschendorf
      Pages 227-263
    3. Ludger Rüschendorf
      Pages 305-322
  5. Optimal Portfolios and Extreme Risks

    1. Front Matter
      Pages 323-324
    2. Ludger Rüschendorf
      Pages 325-351
  6. Back Matter
    Pages 385-408

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.  


62P05 , 91B30 , 91B28 ,60G70 Fréchet-classes mathematical risk analysis optimal portfolios and insurance contracts risk bounds risk measures

Authors and affiliations

  • Ludger Rüschendorf
    • 1
  1. 1.Department of Mathematical StochasticsUniversity of FreiburgFreiburgGermany

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-33589-1
  • Online ISBN 978-3-642-33590-7
  • Series Print ISSN 1431-8598
  • Buy this book on publisher's site
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