Rent 9781405183697 | A Probability Metrics Approach to Financial Risk Measures | Rachev, Svetlozar T.; Stoyanov, Stoyan V.; Fabozzi, Frank J. @knetbooks.com

Summary Table of Contents Author Biography

Is the behavior of the stocks in our portfolio close to their behavior during the most recent crisis? How close is the strategy of hedge fund A to the strategy of hedge fund B? In which proportions do we invest in a given universe of stocks so that the resulting portfolio matches as much as possible the strategy of fund C?All of these questions are essential to finance and they have one feature in common: measuring distances between random quantities. Problems of this kind have been explored for many years in areas other than finance. In A Prob... MORE

Introduction
Probability metrics
Applications in finance
Probability distances and metrics
Introduction
Some examples of probability metrics
Engineer's metric
Uniform
Levy metric
Kantorovich metric
Lp-metrics between distribution functions
Ky Fan me... MOREtrics
Lp-metric
Distance and semidistance spaces
Definitions of probability distances and metrics
Summary
Technical appendix
Universally measurable separable metric spaces
The equivalence of the notions of p. (semi-)distance on P2 and on X
Choice under uncertainty
Introduction
Expected utility theory
St. Petersburg Paradox
The von Neumann-Morgenstern expected utility theory
Types of utility functions
Stochastic dominance
First-order stochastic dominance
Second-order stochastic dominance
Rothschild-Stiglitz stochastic dominance
Third-order stochastic dominance
Efficient sets and the portfolio choice problem
Return versus payoff
Probability metrics and stochastic dominance
Cumulative Prospect Theory
Summary
Technical appendix
The axioms of choice
Stochastic dominance relations of order n
Return versus payoff and stochastic dominance
Other stochastic dominance relations
A classification of probability distances
Introduction
Primary distances and primary metrics
Simple distances and metrics
Compound distances and moment functions
Ideal probability metrics
Interpretation and examples of ideal probability metrics
Conditions for boundedness of ideal probability metrics
Summary
Technical appendix
Examples of primary distances
Examples of simple distances
Examples of compound distances
Examples of moment functions
Risk and uncertainty
Introduction
Measures of dispersion
Standard deviation
Mean absolute deviation
Semi-standard deviation
Axiomatic description
Deviation measures
Probability metrics and dispersion measures
Measures of risk
Value-at-risk
Computing portfolio VaR in practice
Back-testing of VaR
Coherent risk measures
Risk measures and dispersion measures
Risk measures and stochastic orders
Summary
Technical appendix
Convex risk measures
Probability metrics and deviation measures
Deviation measures and probability quasi-metrics
Average value-at-risk
Introduction
Average value-at-risk
AVaR for stable distributions
AVaR estimation from a sample
Computing portfolio AVaR in practice
The multivariate normal assumption
The Historical Method
The Hybrid Method
The Monte Carlo Method
Kernel methods
Back-testing of AVaR
Spectral risk measures
Risk measures and probability metrics
Risk measures based on distortion functionals
Summary
Technical appendix
Characteristics of conditional loss distributions
Higher-order AVaR
The minimization formula for AVaR
ETL vs AVaR
Kernel-based estimation of AVaR
Remarks on spectral risk measures
Computing AVaR through Monte Carlo
Introduction
An illustration of Monte Carlo variability
Asymptotic distribution, classical conditions
Rate of convergence to the normal distribution
The effect of tail thickness
The effect of tail truncation
Infinite variance distributions
Asymptotic distribution, heavy-tailed returns
Rate of convergence, heavy-tailed returns
Stable Paretian distributions
Student's t distribution
On the choice of a distributional model
Tail behavior and return frequency
Practical implications
Summary
Technical appendix
Proof of the stable limit result
Stochastic dominance revisited
Introduction
Metrization of preference relations
The Hausdorff metric structure
Examples
The Levy quasi-semidistance and first-order stochastic dominance
Higher order stochastic dominance
The H-quasi-semidistance
AVaR generated stochastic orders
Compound quasi-semidistances
Utility-type representations
Almost stochastic orders and degree of violation
Summary
Technical appendix
Preference relations and topology
Quasi-semidistances and preference relations
Construction of quasi-semidistances on classes of investors
Investors with balanced views
Structural classification of probability distances
Table of Contents provided by Publisher. All Rights Reserved.

Svetlozar T. Rachev is Chair-Professor in Statistics, Econometrics and Mathematical Finance at the University of Karlsruhe in the School of Economics and Business Engineering. Stoyan V. Stoyanov is a Professor of Finance at EDHEC Business School and Scientific Director for EDHEC-Risk Institute in Asia. Frank J. Fabozzi is Professor in the Practice of Finance in the School of Management at Yale University.

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