Model risk management : risk bounds under uncertainty / Ludger Rüschendorf, Steven Vanduffel, Carole Bernard.

Format:

Book

Author/Creator:

Rüschendorf, Ludger, 1948- author.

Vanduffel, Steven, author.

Bernard, Carole, author.

Language:

English

Subjects (All):

Risk management.

Management.

Computer simulation.

Physical Description:

1 online resource (xxi, 323 pages) : digital, PDF file(s).

Edition:

First edition.

Place of Publication:

Cambridge : Cambridge University Press, 2024.

Summary:

This book provides the first systematic treatment of model risk, outlining the tools needed to quantify model uncertainty, to study its effects, and, in particular, to determine the best upper and lower risk bounds for various risk aggregation functionals of interest. Drawing on both numerical and analytical examples, this is a thorough reference work for actuaries, risk managers, and regulators. Supervisory authorities can use the methods discussed to challenge the models used by banks and insurers, and banks and insurers can use them to prioritize the activities on model development, identifying which ones require more attention than others. In sum, it is essential reading for all those working in portfolio theory and the theory of financial and engineering risk, as well as for practitioners in these areas. It can also be used as a textbook for graduate courses on risk bounds and model uncertainty.

Contents:

Cover

Half-title

Title page

Imprints page

Contents

Preface

Introduction

Part I Risk Bounds for Portfolios Based on Marginal Information

1 Risk Bounds with Known Marginal Distributions

1.1 Some Basic Notions and Results of Risk Analysis

1.2 Standard Bounds, VaR Bounds, and Worst Case Distributions

1.3 Worst Case Risk Vectors: The Conditional Moment Method and the Mixing Method

1.4 Mixability and Convex Minima of Portfolios

2 The Rearrangement Algorithm

2.1 Formulation of Dependence Problems as Rearrangement Problems

2.2 The Rearrangement Algorithm

2.3 The Block Rearrangement Algorithm

3 Dual Bounds

3.1 Hoeffding-Fréchet Functionals

3.2 Dual Representation of Hoeffding-Fréchet Functionals

3.3 Sharpness of the Dual Bounds for the Tail Risk

4 Asymptotic Equivalence Results

4.1 Introduction and Motivation

4.2 Asymptotics for Conservative Capital Charges: The Homogeneous Finite Mean Case

4.3 Asymptotics for VaR in the Infinite Mean Case

4.4 Asymptotic Equivalence in the Inhomogeneous Case

Part II Additional Dependence Constraints

5 Improved Standard Bounds

5.1 Standard and Improved Standard Bounds for Monotonic Functions

5.2 Computation of Improved Standard Bounds

5.3 VaR Bounds with Two-Sided Dependence Information

6 VaR Bounds with Variance Constraints

6.1 VaR Bounds with an Upper Bound on the Variance

6.2 Algorithm to Approximate VaR Bounds

6.3 Generalization to Constraints on Higher Moments on Default Probabilities

6.4 Discussion of Consequences for Credit Risk Modeling

7 Distributions Specified on a Subset

7.1 Improved Hoeffding-Fréchet Bounds

7.2 Distribution Functions or Copulas with Given Bounds on a Subset

7.3 Distributions Known on a Subset

Part III Additional Information on the Structure.

8 Additional Information on Functionals of the Risk Vector

8.1 Higher-Dimensional Marginals

8.2 Functionals of the Risk Vector

9 Partially Specified Risk Factor Models

9.1 Partially Specified Factor Models

9.2 Risk Bounds

9.3 Bounds for Convex Risk Measures

9.4 Relation between VaR and TVaR Bounds

9.5 Application to Credit Risk Portfolios

10 Models with a Specified Subgroup Structure

10.1 Subgroup Models with Positive and Negative Internal Dependence

10.2 Models with Independent Subgroups

10.3 VaR Bounds in Subgroup Models with Dependence Information within and between the Subgroups

Part IV Risk Bounds under Moment Information

11 Bounds on VaR, TVaR, and RVaR under Moment Information

11.1 VaR Bounds: Bounded Domain

11.2 VaR Bounds: Unbounded Domain

11.3 TVaR and RVaR Bounds

11.4 Proofs

12 Bounds for Distortion Risk Measures under Moment Information

12.1 Bounds for Distortion Risk Measures: Bounded Domain

12.2 Bounds for Distortion Risk Measures: Unbounded Domain

12.3 Proofs

13 Bounds for VaR, TVaR, and RVaR under Unimodality Constraints

13.1 VaR Bounds

13.2 RVaR and TVaR Bounds

13.3 Application to Model Risk Assessment of a Credit Risk Portfolio

13.4 Proofs

14 Moment Bounds in Neighborhood Models

14.1 Problem Formulation

14.2 Bounds on Distortion Risk Measures

14.3 Bounds on Range VaR

14.4 Application to an Insurance Portfolio

14.5 Proofs

14.6 Appendix: Isotonic Projection

14.7 Appendix: Models for Insurance Portfolio Losses

References

Index.

Notes:

Title from publisher's bibliographic system (viewed on 02 Jan 2024).

Includes bibliographical references and index.

ISBN:

9781009367202

100936720X

9781009367189

1009367188

OCLC:

1481138699