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Mathematical Risk Analysis

Dependence, Risk Bounds, Optimal Allocations and Portfolios

  • Book
  • © 2013

Overview

Authors:
  1. Ludger Rüschendorf

    1. Department of Mathematical Stochastics, University of Freiburg, Freiburg, Germany

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  • 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?
  • Includes supplementary material: sn.pub/extras

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xii
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  2. Stochastic Dependence and Extremal Risk

    1. Front Matter

      Pages 1-2
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    2. Copulas, Sklar’s Theorem, and Distributional Transform

      • Ludger Rüschendorf
      Pages 3-34

    3. Fréchet Classes, Risk Bounds, and Duality Theory

      • Ludger Rüschendorf
      Pages 35-51

    4. Convex Order, Excess of Loss, and Comonotonicity

      • Ludger Rüschendorf
      Pages 53-70

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

      • Ludger Rüschendorf
      Pages 71-90

    6. Restrictions on the Dependence Structure

      • Ludger Rüschendorf
      Pages 91-112

    7. Dependence Orderings of Risk Vectors and Portfolios

      • Ludger Rüschendorf
      Pages 113-136

  3. Risk Measures and Worst Case Portfolios

    1. Front Matter

      Pages 137-140
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    2. Risk Measures for Real Risks

      • Ludger Rüschendorf
      Pages 141-165

    3. Risk Measures for Portfolio Vectors

      • Ludger Rüschendorf
      Pages 167-188

    4. Law Invariant Convex Risk Measures on \(L_{d}^{p}\) and Optimal Mass Transportation

      • Ludger Rüschendorf
      Pages 189-221

  4. Optimal Risk Allocation

    1. Front Matter

      Pages 223-225
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    2. Optimal Allocations and Pareto Equilibrium

      • Ludger Rüschendorf
      Pages 227-263

    3. Characterization and Examples of Optimal Risk Allocations for Convex Risk Functionals

      • Ludger Rüschendorf
      Pages 265-303

    4. Optimal Contingent Claims and (Re)insurance Contracts

      • Ludger Rüschendorf
      Pages 305-322

  5. Optimal Portfolios and Extreme Risks

    1. Front Matter

      Pages 323-324
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    2. Optimal Portfolio Diversification w.r.t. Extreme Risks

      • Ludger Rüschendorf
      Pages 325-351

    3. Ordering of Multivariate Risk Models with Respect to Extreme Portfolio Losses

      • Ludger Rüschendorf
      Pages 353-383

  6. Back Matter

    Pages 385-408
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Keywords

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.      

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)

Authors and Affiliations

  • Department of Mathematical Stochastics, University of Freiburg, Freiburg, Germany

    Ludger Rüschendorf

About the author

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.

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