Optimal expected utility risk measures

References

[1] C. Acerbi and D. Tasche, On the coherence of expected shortfall, J. Bank. Finance 26 (2002), no. 7, 1487–1503. 10.1016/S0378-4266(02)00283-2Suche in Google Scholar

[2] K. J. Arrow, Essays in the Theory of Risk-Bearing, 3rd ed., Markham, Chicago, 1971. Suche in Google Scholar

[3] P. Artzner, F. Delbaen, J.-M. Eber and D. Heath, Thinking coherently, Risk Mag. 10 (1997), no. 11, 68–72. Suche in Google Scholar

[4] P. Artzner, F. Delbaen, J.-M. Eber and D. Heath, Coherent measures of risk, Math. Finance 9 (1999), no. 3, 203–228. 10.1111/1467-9965.00068Suche in Google Scholar

[5] P. Barrieu and N. E. Karoui, Pricing, hedging and optimally designing derivatives via minimization of risk measures, Indifference Pricing: Theory and Applications, Princeton University Press, Princeton (2008), 77–146. 10.1515/9781400833115.77Suche in Google Scholar

[6] H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer, New York, 2011. 10.1007/978-1-4419-9467-7Suche in Google Scholar

[7] F. Bellini, B. Klar, A. Müller and E. R. Gianin, Generalized quantiles as risk measures, Insurance Math. Econom. 54 (2014), 41–48. 10.1016/j.insmatheco.2013.10.015Suche in Google Scholar

[8] A. Ben-Tal and M. Teboulle, Expected utility, penalty functions and duality in stochastic nonlinear programming, Manag. Sci. 32 (1986), no. 11, 1445–1466. 10.1287/mnsc.32.11.1445Suche in Google Scholar

[9] A. Ben-Tal and M. Teboulle, An old-new concept of convex risk measures: The optimized certainty equivalent, Math. Finance 17 (2007), no. 3, 449–476. 10.1111/j.1467-9965.2007.00311.xSuche in Google Scholar

[10] P.-A. Chiappori and M. Paiella, Relative risk aversion is constant: Evidence from panel data, J. Eur. Econ. Assoc. 9 (2011), no. 6, 1021–1052. 10.1111/j.1542-4774.2011.01046.xSuche in Google Scholar

[11] B. de Finetti, Sul Concetto di Media, Giorn. Ist. Ital. Attuari 2 (1931), 369–396. Suche in Google Scholar

[12] F. Delbaen, Coherent Risk Measures, Scuola Normale Superiore, Pisa, 2000. Suche in Google Scholar

[13] F. Delbaen, Coherent risk measures on general probability spaces, Advances in Finance and Stochastics, Springer, Berlin (2002) 1–37. 10.1007/978-3-662-04790-3_1Suche in Google Scholar

[14] K. Detlefsen and G. Scandolo, Conditional and dynamic convex risk measures, Finance Stoch. 9 (2005), no. 4, 539–561. 10.1007/s00780-005-0159-6Suche in Google Scholar

[15] H. Fink, S. Geissel, J. Sass and F. T. Seifried, Implied risk aversion: An alternative rating system for retail structured products, preprint (2017), http://ssrn.com/abstract=2651135. Suche in Google Scholar

[16] P. C. Fishburn, Utility Theory for Decision Making, Wiley, New York, 1970. 10.21236/AD0708563Suche in Google Scholar

[17] P. C. Fishburn, Nonlinear Preference and Utility Theory, Johns Hopkins University Press, Baltimore, 1988. Suche in Google Scholar

[18] H. Föllmer and T. Knispel, Entropic risk measures: Coherence vs. convexity, model ambiguity, and robust large deviations, Stoch. Dyn. 11 (2011), no. 2–3, 333–351. 10.1142/S0219493711003334Suche in Google Scholar

[19] H. Föllmer and A. Schied, Convex measures of risk and trading constraints, Finance Stoch. 6 (2002), no. 4, 429–447. 10.1007/s007800200072Suche in Google Scholar

[20] H. Föllmer and A. Schied, Stochastic Finance, 3rd ed., De Gruyter, Berlin, 2011. 10.1515/9783110218053Suche in Google Scholar

[21] I. Friend and M. E. Blume, The demand for risky assets, Amer. Econ. Rev. 65 (1975), no. 5, 900–922. 10.1016/B978-0-12-445850-5.50008-8Suche in Google Scholar

[22] M. Fritelli and E. Rosazza Gianin, Putting order in risk measures, J. Bank. Finance 26 (2002), no. 7, 1473–1486. 10.1016/S0378-4266(02)00270-4Suche in Google Scholar

[23] S. Geissel, Utility-Based Risk Measures and Time Consistency of Dynamic Risk Measures, Dissertation, TU Kaiserslautern, 2015. Suche in Google Scholar

[24] K. Giesecke, T. Schmidt and S. Weber, Measuring the risk of large losses, J. Investment Manag. 6 (2008), no. 4, 1–15. Suche in Google Scholar

[25] C. Gollier, The Economics of Risk and Time, MIT Press, Cambridge, 2001. 10.7551/mitpress/2622.001.0001Suche in Google Scholar

[26] D. Heath, Back to the future, Plenary lecture at the First World Congress of the Bachelier Society, 2000. 10.7748/eldc.9.1.41.s36Suche in Google Scholar PubMed

[27] D. Heath and H. Ku, Pareto equilibria with coherent measures of risk, Math. Finance 14 (2004), no. 2, 163–172. 10.1111/j.0960-1627.2004.00187.xSuche in Google Scholar

[28] E. Jouini, W. Schachermayer and N. Touzi, Law invariant risk measures have the Fatou property, Advances in Mathematical Economics, Springer, Tokyo (2006), 49–71. 10.1007/4-431-34342-3_4Suche in Google Scholar

[29] M. S. Kimball, Precautionary saving in the small and in the large, Econometrica 58 (1990), no. 1, 53–73. 10.2307/2938334Suche in Google Scholar

[30] M. S. Kimball, Standard risk aversion, Econometrica 61 (1993), no. 3, 589–611. 10.2307/2951719Suche in Google Scholar

[31] P. A. Krokhmal, Higher moment coherent risk measures, Quant. Finance 7 (2007), no. 4, 373–387. 10.1080/14697680701458307Suche in Google Scholar

[32] A. Mas-Colell, M. D. Whinston and J. R. Green, Microeconomic Theory, Oxford University Press, Oxford, 1995. Suche in Google Scholar

[33] D. J. Meyer and J. Meyer, Relative risk aversion: What do we know?, J. Risk Uncertain. 31 (2005), no. 3, 243–262. 10.1007/s11166-005-5102-xSuche in Google Scholar

[34] A. Müller, Certainty equivalents as risk measures, Braz. J. Probab. Stat. 21 (2007), no. 1, 1–12. Suche in Google Scholar

[35] M. Nagumo, Über eine Klasse der Mittelwerte, Jpn. J. Math. 7 (1930), 71–79. 10.4099/jjm1924.7.0_71Suche in Google Scholar

[36] J. W. Pratt, Risk aversion in the small and in the large, Econometrica 32 (1964), no. 1–2, 122–136. 10.2307/1913738Suche in Google Scholar

[37] R. T. Rockafellar and S. Uryasev, Optimization of conditional value-at-risk, J. Risk 2 (2000), no. 3, 21–41. 10.21314/JOR.2000.038Suche in Google Scholar

[38] R. T. Rockafellar and S. Uryasev, Conditional value-at-risk for general loss distributions, J. Bank. Finance 26 (2002), no. 7, 1443–1471. 10.1016/S0378-4266(02)00271-6Suche in Google Scholar

[39] G. G. Szpiro, Measuring risk aversion: An alternative approach, Rev. Econ. Stat. 68 (1986), 156–159. 10.2307/1924939Suche in Google Scholar

[40] A. Vinel and P. A. Krokhmal, Certainty equivalent measures of risk, Ann. Oper. Res. 249 (2017), no. 1–2, 75–95. 10.1007/s10479-015-1801-0Suche in Google Scholar

[41] J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, 2nd ed., Princeton University Press, Princeton, 1947. Suche in Google Scholar

[42] S. Weber, Distribution-invariant risk measures, information, and dynamic consistency, Math. Finance 16 (2006), no. 2, 419–441. 10.1111/j.1467-9965.2006.00277.xSuche in Google Scholar