Orderings and Probability Functionals Consistent with Preferences

References

• Acerbi , C. 2002 . Spectral measures of risk:  A coherent representation of subjective risk aversion. . Journal of Banking and Finance , 26 (7) : 1505 – 1518 .
   Web of Science ®Google Scholar
• Artzner , P. , Delbaen , F. , Eber , J.‐M. and Heath , D. 1997 . Thinking coherently. . Risk , 10 (11) : 68 – 71 .
   Google Scholar
• Artzner , P. , Delbaen , F. , Eber , J.‐M. and Heath , D. 1999 . Coherent measures of risk. . Mathematical Finance , 9 (3) : 203 – 228 .
   Web of Science ®Google Scholar
• Baucells , M. and Heukamp , F. H. 2006 . Stochastic dominance and cumulative prospect theory. . Management Science , 52 (9) : 1409 – 1423 .
   Web of Science ®Google Scholar
• Blackwell , D. and Girshick , M. A. 1979 . Theory of Games and Statistical Decisions , New York : Dover Publications . reprint of the 1954 edition
   Google Scholar
• Bordley , R. and LiCalzi , M. 2000 . Decision analysis using targets instead of utility functions. . Decisions in Economics and Finance , 23 (1) : 53 – 74 .
   Google Scholar
• Cambanis , S. , Simons , G. and Stout , W. 1976 . Inequalities for Ek(x,y) when the marginals are fixed. . Zeitschrift fur Wahrscheinlichkeitstheorie und verwandte Gebiete , 36 (4) : 285 – 294 .
   Google Scholar
• Castagnoli , E. and LiCalzi , M. 1999 . Nonexpected utility theories and benchmarking under risk. . SZIGMA , 29 : 199 – 211 .
   Google Scholar
• Edwards , K. D. 1996 . Prospect theory :  A literature review. . International Review of Financial Analysis , 5 (1) : 19 – 38 .
   Google Scholar
• Fishburn , P. C. 1976 . Continua of stochastic dominance relations for bounded probability distributions. . Journal of Mathematical Economics , 3 (3) : 295 – 311 .
   Google Scholar
• Fishburn , P. C. 1980 . Continua of stochastic dominance relations for unbounded probability distributions. . Journal of Mathematical Economics , 7 (3) : 271 – 285 .
   Web of Science ®Google Scholar
• Föllmer , H. and Sheid , A. 2002a . Convex measures of risk and trading constraints. . Finance and Stochastics , 6 (4) : 429 – 447 .
   Web of Science ®Google Scholar
• Föllmer , H. and Sheid , A. 2002b . Stochastic Finance :  An Introduction in Discrete Time , Berlin : Walter de Gruyter .
   Google Scholar
• Friedman , M. and Savage , L. J. 1948 . The utility analysis of choices involving risk. . Journal of Political Economy , 56 : 279 – 304 .
   Web of Science ®Google Scholar
• Geyer , A. and Ziemba , W. T. 2008 . The Innovest Austrian pension fund financial planning model InnoALM. . Operations Research , 56 (4)
   PubMed Web of Science ®Google Scholar
• Gilboa , I. and Schmeidler , D. 1989 . Maxmin expected utility with non‐unique prior. . Journal of Mathematical Economics , 18 : 141 – 153 .
   Web of Science ®Google Scholar
• Hardy , G. H. , Littlewood , J. E. and Polya , G. 1934 . Inequalities , Cambridge : Cambridge University Press .
   Google Scholar
• Karni , E. 1985 . Decision Making Under Uncertainty :  The Case of State‐Dependent Preferences , Cambridge : Harvard University Press .
   Google Scholar
• Kashnikov , V. and Rachev , S. 1988 . Mathematical Methods for Construction for Queueing Models (Moscow, Nauka) (in Russian), English trans. (Wadsworth & Brooks/Cole Advanced Books, 1990)
   Google Scholar
• Levy , H. 1992 . Stochastic dominance and expected utility :  Survey and analysis. . Management Science , 38 (4) : 555 – 593 .
   Web of Science ®Google Scholar
• Levy , M. and Levy , H. 2002 . Prospect theory :  Much ado about nothing? . Management Science , 48 (10) : 1334 – 1349 .
   Web of Science ®Google Scholar
• Maccheroni , F. , Marinacci , M. , Rustichini , A. and Toboga , M. 2004 . Portfolio selection with monotone mean‐variance preferences. . ICER Working paper 27, Torino
   Google Scholar
• Machina , M. J. 1982 . Expected utility analysis without the independence axiom. . Econometrica , 50 : 277 – 323 .
   Web of Science ®Google Scholar
• Markowitz , H. M. 1952 . The utility of wealth. . Journal of Political Economy , 60 (2) : 151 – 156 .
   Web of Science ®Google Scholar
• Miller , K. S. and Ross , B. 1993 . An Introduction to the Fractional Calculus and Fractional Differential Equation , New York : Wiley .
   Google Scholar
• Muliere , P. and Scarsini , M. 1989 . A note on stochastic dominance and inequality measures. . Journal of Economic Theory , 49 (2) : 314 – 323 .
   Web of Science ®Google Scholar
• Müller , A. 1997 . Stochastic orders generated by integrals :  A unified study. . Advances in Applied Probability , 29 (2) : 414 – 428 .
   Web of Science ®Google Scholar
• Müller , A. and Stoyan , D. 2002 . Comparison Methods for Stochastic Models and Risks , New York : Wiley .
   Google Scholar
• Ortobelli , S. , Rachev , S. , Shalit , H. and Fabozzi , F. 2006 . Risk probability functionals and probability metrics applied to portfolio theory, Working Paper, Department of Probability and Applied Statistics, University of California, Santa Barbara
   Google Scholar
• Ortobelli , S. , Rachev , S. , Shalit , H. and Fabozzi , F. 2008 . The theory of orderings and risk probability functionals. . Probability and Mathematical Statistics , forthcoming
   Google Scholar
• Rabin , M. 2000 . Risk aversion and expected utility theory :  A calibration theorem. . Econometrica , 68 (5) : 1281 – 1292 .
   Web of Science ®Google Scholar
• Rabin , M. and Thaler , R. 2001 . Anomalies :  Risk aversion. . Journal of Economic Perspectives , 15 (1) : 219 – 232 .
   Web of Science ®Google Scholar
• Rachev , S. 1991 . Probability Metrics and the Stability of Stochastic Models , Chichester : Wiley .
   Google Scholar
• Rachev , S. , Ortobelli , S. , Stoyanov , S. , Fabozzi , F. and Biglova , A. 2008 . Desirable properties of an ideal risk measure in portfolio theory. . International Journal of Theoretical and Applied Finance , 11 (1) : 19 – 54 .
   Google Scholar
• Rockafellar , R. T. and Ziemba , W. T. 2000 . Modified risk measures and acceptance sets, Unpublished manuscript .
   Google Scholar
• Rockafellar , R. T. , Uryasev , S. and Zabarankin , M. 2006 . Generalized deviations in risk analysis. . Finance and Stochastics , 10 (1) : 51 – 74 .
   Web of Science ®Google Scholar
• Rothschild , M. and Stiglitz , J. 1970 . Increasing risk I:  Definition. . Journal of Economic Theory , 2 (3) : 225 – 243 .
   Web of Science ®Google Scholar
• Schervisch , M. J. , Seidenfeld , T. and Kadane , J. B. 1990 . State‐dependent utilities. . Journal of the American Statistical Association , 85 (411) : 840 – 847 .
   Web of Science ®Google Scholar
• Shaked , M. and Shanthikumar , G. 1994 . Stochastic Orders and Their Applications , New York : Academic Press .
   Google Scholar
• Shaked , M. and Shanthikumar , G. 2006 . Stochastic Orders , New York : Springer .
   Google Scholar
• Stoyanov , S. , Rachev , S. , Ortobelli , S. and Fabozzi , F. 2008 . Relative deviation metrics and the problem of strategy replication. . Journal of Banking and Finance , 32 (2) : 199 – 206 .
   Web of Science ®Google Scholar
• Szegö , G. 2004 . Risk Measures for the 21^st Century , Chichester : Wiley .
   Google Scholar
• Tversky , A. and Kahneman , D. 1992 . Advances in prospect theory:  Cumulative representation of uncertainty. . Journal of Risk and Uncertainty , 5 (4) : 297 – 323 .
   Web of Science ®Google Scholar
• Von Neumann , J. and Morgenstern , O. 1953 . Theory of Games and Economic Behavior , Princeton, NJ : Princeton University Press .
   Google Scholar
• Yaari , M. 1987 . The dual theory of choice under risk. . Econometrica , 55 (1) : 95 – 115 .
   Web of Science ®Google Scholar