MODELING,MEASURING & MANAGING RISK

By: PFLUG GEORG CH

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Hardcover | 14 August 2007

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Hardcover
304 Pages

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22.86 x 15.24 x 1.75

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This book is the first in the market to treat single- and multi-period risk measures (risk functionals) in a thorough, comprehensive manner. It combines the treatment of properties of the risk measures with the related aspects of decision making under risk.The book introduces the theory of risk measures in a mathematically sound way. It contains properties, characterizations and representations of risk functionals for single-period and multi-period activities, and also shows the embedding of such functionals in decision models and the properties of these models.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Business & Management Management & Management Techniques Management Decision Making Society & Social Sciences Reference, Information & Interdisciplinary Subjects Research & Information Decision Theory Applied Mathematics

Mathematical Modelling Operational Research Probability & Statistics Booktopia Publisher Services World Scientific Publishing

Preface	p. vii
List of Symbols	p. ix
Modeling uncertain outcomes	p. 1
The three M's of decision making under uncertainty	p. 1
Probability models and scenario distributions	p. 4
Distribution functions and quantile functions	p. 6
Joint distributions and couplings	p. 8
Utility functions and order relations	p. 12
Compounding	p. 20
Standard statistical parameters	p. 21
Location parameters	p. 21
Dispersion parameters	p. 22
Correlation parameters	p. 24
Measuring single-period risk	p. 27
Probability functionals and their properties	p. 27
Properties of probability functionals	p. 29
Version-independent properties of probability functionals	p. 31
Acceptability functionals and deviation risk functionals	p. 35
Acceptance sets for translation-equivariant functionals	p. 39
Dual representations of concave and convex functionals	p. 41
The average value-at-risk	p. 48
Kusuoka representations	p. 58
Conditional acceptability and risk mappings	p. 66
Version independent conditional acceptability mappings	p. 73
More about the conditional average value-at-risk	p. 75
Classes of version-independent acceptability-type functionals	p. 77
Expected utility	p. 78
Distortion functionals	p. 80
Sup-convolutions	p. 88
Single-period polyhedral acceptability functionals	p. 91
Risk-corrected expectation and mean-risk models	p. 93
Classes of version-independent deviation-type functionals	p. 94
Deviation functionals of the form E[h(Y - EY)]	p. 95
Deviation functionals of the form Y - EY [subscript h]	p. 99
Deviation functionals of the form [Y - EY superscript -] [subscript h]	p. 102
Deviation functionals of the form E[h(Y - Y[prime])]	p. 106
Minimal loss risk functionals	p. 107
Summary	p. 112
Measuring multi-period risk	p. 115
Introduction to multi-period models	p. 115
Evolving information: filtrations and tree processes	p. 119
Dynamic acceptability functionals	p. 124
Introducing information into single-period functionals	p. 126
Multi-period risk functionals: basic properties	p. 132
Dual representations of multi-period acceptability functionals	p. 136
Version-independent multi-period risk functionals	p. 140
Classes of multi-period acceptability functionals	p. 144
Separable functionals	p. 144
Risk functionals of the value-of-information type	p. 146
More about the multi-period average value-at-risk	p. 150
Composition of conditional acceptability mappings	p. 154
Polyhedral multi-period acceptability functionals	p. 159
Polyhedral acceptability functionals in multi-stage stochastic programs	p. 169
Summary	p. 172
Single-stage decision models	p. 175
Stochastic optimization	p. 175
Efficient frontiers	p. 179
Simple deviation risk models	p. 183
Discrete models	p. 187
Standard deviation efficiency	p. 188
Lower standard deviation efficiency	p. 196
Mean absolute deviation efficiency	p. 198
Average value-at-risk deviation efficiency	p. 198
Value-at-risk deviation efficiency	p. 200
Minimal loss efficiency	p. 201
Distortion efficiency	p. 202
Risk contributions	p. 205
Multi-stage decision models for financial management	p. 211
Multi-stage decisions	p. 211
Tree models	p. 216
A typical multi-stage financial optimization problem	p. 217
Value-of-information: standard and clairvoyant problems	p. 221
Acceptability and value-of-information processes	p. 223
An example for a value-of-information process	p. 224
Efficient frontiers in multi-stage portfolio optimization	p. 229
A multi-stage insurance model	p. 233
Multi-stage decision models for electricity management	p. 245
Introduction	p. 245
Case study: Mean-risk portfolio optimization of a municipal power utility	p. 247
Optimization model	p. 251
Objective and multi-period polyhedral acceptability functionals	p. 258
Simulation results	p. 260
Conclusions	p. 263
Probability spaces, [sigma]-fields and L[subscript p]-spaces	p. 265
Fenchel-Moreau duality	p. 269
Description of the data set used in Chapters 4 and 5	p. 273
Bibliography	p. 277
Index	p. 285
Table of Contents provided by Ingram. All Rights Reserved.

MODELING,MEASURING & MANAGING RISK

At a Glance

Hardcover

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