Entropy Coherent and Entropy Convex Measures of Risk
Published Online:24 Oct 2012https://doi.org/10.1287/moor.1120.0559
References
- . A definition of subjective probability. Ann. Math. Statist. (1963) 34(1):199–205Crossref, Google Scholar
- . Coherent measures of risk. Math. Finance (1999) 9(3):203–228Crossref, Google Scholar
- . Inf-convolution of risk measures and optimal risk transfer. Finance Stochastics (2005) 9(2):269–298Crossref, Google Scholar
- . Expected utility, penalty functions, and duality in stochastic nonlinear programming. Management Sci. (1986) 32(11):1445–1466Link, Google Scholar
- . Penalty functions and duality in stochastic programming via φ-divergence functionals. Math. Oper. Res. (1987) 12(2):224–240Link, Google Scholar
- . An old-new concept of convex risk measures: The optimized certainty equivalent. Math. Finance (2007) 17(3):449–476Crossref, Google Scholar
- . Equilibrium in a reinsurance market. Econometrica (1962) 30(3):424–444Crossref, Google Scholar
- . Uncertainty averse preferences. J. Econom. Theory (2011) 146(4):1275–1330Crossref, Google Scholar
- . Risk measures: Rationality and diversification. Math. Finance (2011) 21(4):743–774Google Scholar
- . Ambiguity through confidence functions. J. Math. Econom. (2010) 45(9–10):535–558Crossref, Google Scholar
- . Recursiveness of indifference prices and translation-invariant preferences. Math. Financial Econom. (2009) 2(3):173–188Crossref, Google Scholar
- . I-divergence geometry of probability distributions and minimization problems. Ann. Probab. (1975) 3(1):146–158Crossref, Google Scholar
- . A representation result for concave Schur concave functions. Math. Finance (2005) 15(4):613–634Crossref, Google Scholar
- . On convex principles of premium calculation. Insurance: Math. Econom. (1985) 4(3):179–189Crossref, Google Scholar
- . Linear Operators. Part I: General Theory (1958) (Wiley Interscience, New York) Google Scholar
- . Cash subadditive risk measures and interest rate ambiguity. Math. Finance (2009) 19(4):561–590Crossref, Google Scholar
- . Convex measures of risk and trading constraints. Finance Stochastics (2002) 6(4):429–447Crossref, Google Scholar
- . Stochastic Finance (2004) 2nd ed.(De Gruyter, Berlin) Crossref, Google Scholar
- , Ciarlet P, Bensoussan A, Zhang Q. Robust preferences and robust portfolio choice. Mathematical Modelling and Numerical Methods in Finance. Handbook of Numerical Analysis (2009) 15:29–88Google Scholar
- . Putting order in risk measures. J. Banking and Finance (2002) 26(7):1473–1486Crossref, Google Scholar
- . Risk measures and capital requirements for processes. Math. Finance (2006) 16(4):589–612Crossref, Google Scholar
- . An Introduction to Mathematical Risk Theory (1979) (Irwin, Homewood, IL) S.S. Huebner Foundation Monograph 8Google Scholar
- . On additive principles of zero utility. Insurance: Math. Econom. (1985) 4(4):249–251Crossref, Google Scholar
- . Maxmin expected utility with nonunique prior. J. Math. Econom. (1989) 18(2):141–153Crossref, Google Scholar
- . The Economics of Risk and Time (2001) (MIT Press, Cambridge, MA) Crossref, Google Scholar
- . Insurance Premiums (1984) (North-Holland Publishing, Amsterdam) Google Scholar
- . A comonotonic image of independence for additive risk measures. Insurance: Math. Econom. (2004) 35(3):581–594Crossref, Google Scholar
- . Robust control and model uncertainty. Amer. Econom. Rev. (2001) 91(2):60–66Crossref, Google Scholar
- . Robustness (2007) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
- . Inequalities (1952) 2nd ed.(Cambridge University Press, Cambridge) Google Scholar
- . Pareto equilibria with coherent measures of risk. Math. Finance (2004) 14(2):163–172Crossref, Google Scholar
- . Robust Statistics (1981) (John Wiley & Sons, New York) Crossref, Google Scholar
- . Ambiguity aversion, robustness, and the variational representation of preferences. Econometrica (2006) 74(6):1447–1498Crossref, Google Scholar
- . Dynamic exponential utility indifference valuation. Ann. Appl. Probab. (2005) 15(3):2113–2143Crossref, Google Scholar
- . Inf-convolution, sous-additivité, convexité des fonctions numériques. Journal de Mathématiques Pures et Appliquées (1970) 49(9):109–154Google Scholar
- . Optimization of conditional value-at-risk. J. Risk (2000) 2(3):21–42Crossref, Google Scholar
- . Risk tuning with generalized linear regression. Math. Oper. Res. (2008) 33(3):712–729Link, Google Scholar
- . Optimization of convex risk functions. Math. Oper. Res. (2006) 31(3):433–452Link, Google Scholar
- . Conditional risk mappings. Math. Oper. Res. (2006) 31(3):544–561Link, Google Scholar
- . The Foundations of Statistics (1954) 2nd ed.(John Wiley & Sons, New York) . 1972, Dover, New YorkGoogle Scholar
- . Axiomatic foundations of multiplier preferences. Econometrica (2011) 79(1):47–73Crossref, Google Scholar
- . Theory of Games and Economic Behavior (1944) 3rd ed.(Princeton University Press, Princeton, NJ) . 1953Google Scholar
- . Statistical Decision Functions (1950) (John Wiley & Sons, New York) Google Scholar
- . Distribution-invariant risk measures, information, and dynamic consistency. Math. Finance (2006) 16(2):419–441Crossref, Google Scholar
- . Convex Analysis in General Vector Spaces (2002) (World Scientific, Singapore) Crossref, Google Scholar

