Measures of risk

The conditions under which the classical measures of risk like the mean, the linear correlation coefficient and VaR can be used are discussed. The definition of risk measure and the main recently proposed risk measures are presented. The problems connected with co-dependence are outlined.

[1]  D. Tasche,et al.  On the coherence of expected shortfall , 2001, cond-mat/0104295.

[2]  Abaxbank,et al.  Spectral Measures of Risk : a Coherent Representation of Subjective Risk Aversion , 2002 .

[3]  Alexander J. McNeil,et al.  Modelling dependent defaults , 2001 .

[4]  Shaun S. Wang,et al.  Axiomatic characterization of insurance prices , 1997 .

[5]  Alan J. Lee,et al.  Generating Random Binary Deviates Having Fixed Marginal Distributions and Specified Degrees of Association , 1993 .

[6]  M. Crouhy,et al.  A comparative analysis of current credit risk models , 2000 .

[7]  P. Embrechts,et al.  Chapter 8 – Modelling Dependence with Copulas and Applications to Risk Management , 2003 .

[8]  I. Olkin,et al.  Families of Multivariate Distributions , 1988 .

[9]  Michael B. Gordy A Comparative Anatomy of Credit Risk Models , 1998 .

[10]  R. Jagannathan,et al.  The Conditional CAPM and the Cross-Section of Expected Returns , 1996 .

[11]  O. Barndorff-Nielsen,et al.  Lévy processes : theory and applications , 2001 .

[12]  M. Frittelli,et al.  Putting order in risk measures , 2002 .

[13]  Carlos E. Testuri,et al.  On Relation between Expected Regret and Conditional Value at Risk , 2000 .

[14]  Emiliano A. Valdez,et al.  Understanding Relationships Using Copulas , 1998 .

[15]  P. Embrechts,et al.  Risk Management: Correlation and Dependence in Risk Management: Properties and Pitfalls , 2002 .

[16]  E. Eberlein,et al.  Hyperbolic distributions in finance , 1995 .

[17]  Thierry Roncalli,et al.  Which Copula is the Right One? , 2000 .

[18]  Abe Sklar,et al.  Random variables, joint distribution functions, and copulas , 1973, Kybernetika.

[19]  Bill Ravens,et al.  An Introduction to Copulas , 2000, Technometrics.

[20]  G. Simons,et al.  On the theory of elliptically contoured distributions , 1981 .

[21]  David S. Jones Emerging problems with the Basel Capital Accord: Regulatory capital arbitrage and related issues☆ , 2000 .

[22]  R. Rockafellar,et al.  Optimization of conditional value-at risk , 2000 .

[23]  Giorgio Szego,et al.  A Critique of the Basel Regulations, or How to Enhance (Im) Moral Hazards , 1999 .

[24]  G. P. Szegö,et al.  Risk measures for the 21st century , 2004 .

[25]  Paul Embrechts,et al.  Extremes and Integrated Risk Management , 2000 .

[26]  Phhilippe Jorion Value at Risk: The New Benchmark for Managing Financial Risk , 2000 .

[27]  H. Joe Multivariate models and dependence concepts , 1998 .

[28]  J. M. Schumacher,et al.  Pricing and hedging in incomplete markets , 2006 .

[29]  Philippe Artzner,et al.  Risk Management: Coherent Measures of Risk , 2002 .

[30]  Mortgage Lending,et al.  Position Paper on the New Basel Capital Accord - Consultative Document from the Basel Committee on Banking Supervision (January 2001) , 2001 .

[31]  Jon Danielsson,et al.  The Cost of Conservatism : Extreme Returns , Value-at-Risk , and the Basle ‘ Multiplication Factor ’ , 1998 .

[32]  E. Altman,et al.  Managing Credit Risk: The Next Great Financial Challenge , 1998 .

[33]  Jon Danielsson,et al.  Incentives for effective risk management , 2002 .

[34]  Katherine Campbell Statistical Analysis of Extreme Values , 2002, Technometrics.

[35]  Stan Uryasev,et al.  Conditional value-at-risk: optimization algorithms and applications , 2000, Proceedings of the IEEE/IAFE/INFORMS 2000 Conference on Computational Intelligence for Financial Engineering (CIFEr) (Cat. No.00TH8520).

[36]  S. Resnick,et al.  Extreme Value Theory as a Risk Management Tool , 1999 .

[37]  Sidney M. Robbins INVESTOR GUIDEPOSTS IN COMPARING INCOME STATEMENTS , 1952 .

[38]  I. Olkin,et al.  A Multivariate Exponential Distribution , 1967 .

[39]  Jon Danielsson,et al.  Value-at-Risk and Extreme Returns , 2000 .

[40]  Helmut Mausser,et al.  Credit risk optimization with Conditional Value-at-Risk criterion , 2001, Math. Program..

[41]  Eric Bouyé,et al.  Copulas for Finance - A Reading Guide and Some Applications , 2000 .

[42]  Clive W. J. Granger,et al.  Large returns, conditional correlation and portfolio diversification: a value-at-risk approach , 2001 .

[43]  C. Goodhart,et al.  An academic response to Basel II , 2001 .

[44]  M. Phelan,et al.  Probability and Statistics Applied to the Practice of Financial Risk Management: The Case of J.P. Morgan's RiskMetrics™ , 1997 .

[45]  Wolfgang Härdle,et al.  Measuring Risk in Complex Stochastic Systems , 2000 .

[46]  Simone Manganelli,et al.  Value at Risk Models in Finance , 2001, SSRN Electronic Journal.

[47]  Alessio Sancetta,et al.  Bernstein Approximations to the Copula Function and Portfolio Optimization , 2001 .

[48]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[49]  Freddy Delbaen,et al.  A Characterization of Measures of Risk , 1997 .

[50]  Jon Danielsson,et al.  The Value of Value at Risk: Statistical, Financial, and Regulatory Considerations , 1998 .

[51]  Marco Scarsini,et al.  Stochastic Comparison of Random Vectors with a Common Copula , 2001, Math. Oper. Res..

[52]  C. Genest,et al.  Statistical Inference Procedures for Bivariate Archimedean Copulas , 1993 .

[53]  Zinoviy Landsman,et al.  Risk measures and insurance premium principles , 2001 .

[54]  David Heath,et al.  Coherent multiperiod risk adjusted values and Bellman’s principle , 2007, Ann. Oper. Res..

[55]  T. Ané,et al.  Dependence Structure and Risk Measure , 2003 .

[56]  R. Nelsen An Introduction to Copulas , 1998 .

[57]  H. Markowitz The optimization of a quadratic function subject to linear constraints , 1956 .

[58]  Harry Joe,et al.  Multivariate Distributions from Mixtures of Max-Infinitely Divisible Distributions , 1996 .

[59]  Jon Danielsson,et al.  On the (Ir)Relevancy of Value-at-Risk Regulation , 2000 .

[60]  Jon Danielsson,et al.  The emperor has no clothes: Limits to risk modelling , 2000 .

[61]  Michael B. Gordy A risk-factor model foundation for ratings-based bank capital rules , 2002 .

[62]  Aleš Černý,et al.  The Theory of Good-Deal Pricing in Financial Markets , 1998 .

[63]  Stanislav Uryasev,et al.  Conditional Value-at-Risk for General Loss Distributions , 2002 .

[64]  Michael B. Gordy Calculation of Higher Moments in CreditRisk + with Applications , 2001 .

[65]  Stefan Huschens,et al.  A stable CAPM in the presence of heavy-tailed distributions , 2000 .