Representation results for law invariant time consistent functions

Mathematics and Financial Economics

Volumn 2, Issue 3, 2009, Pages 189-210

  Kupper, Michael ^a   Schachermayer, Walter ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

Certainty equivalent; Dynamic risk measures; Law invariance; Skorohod embedding theorem; Time consistency

Indexed keywords

EID: 70349677374     PISSN: 18629679     EISSN: 18629660     Source Type: Journal    
DOI: 10.1007/s11579-009-0019-9     Document Type: Article

References (35)

1. Alt F.: Über die Messbarkeit des Nutzens. Zeitschrift für Nationalökonomie. Verlag von Julius Springer, Wien (1935)
2. Artzner Ph., Delbaen F., Eber J.M., Heath D.: Coherent risk measures. Math. Finance 9(3), 203-228 (1999)
3. Artzner P., Delbaen F., Eber J.-M., Heath D., Ku H.: Coherent multiperiod risk adjusted values and Bellman's principle. Ann. Oper. Res. 152, 5-22 (2007)
4. Bernoulli, D.: Specimen theoriae novae de mensura sortis. Commentarii Academiae Scientarum Imperalis Petropolitanae, vol. 5, pp. 175-192 (1738) [Translated by L. Sommer: Econometrica 22 (1954), pp. 23-36]
5. Bullen P.S.: Handbook of Means and Their Inequalities. Kluwer, Dordrecht (2003)
6. Campi L., Schachermayer W.: A super-replication theorem in Kabanov's Model of Transaction Costs. Finance Stoch. 10(4), 579-596 (2006)
7. Cerreia-Vioglio, S., Maccheroni, F., Marinacci, M., Montrucchio, L.: Risk measures: Rationality and diversification (2009, preprint)
8. Cheridito P., Delbaen F., Kupper M.: Dynamic monetary risk measures for bounded discrete-time processes. Electron. J. Probab. 11, 57-106 (2006)
9. Cheridito, P., Kupper, M.: Composition of time-consistent dynamic monetary risk measures in discrete time (2007, preprint)
10. Cheridito P., Li T.: Dual characterization of properties of risk measures on Orlicz hearts. Math. Financial Econ. 2(1), 29-55 (2008)
11. Cheridito P., Stadje M.: Time-inconsistency of VaR and time-consistent alternatives. Finance Res. Lett. 6(1), 40-46 (2009)
12. Delbaen F.: Coherent risk measures on general probability spaces. Advances in Finance and Stochastics, pp. 1-37. Springer, Berlin (2002)
13. Delbaen F.: The structure of m-stable sets and in particular of the set of riskneutral measures. In: Yor, M., Emery, M. (eds) In Memoriam Paul-André Meyer - Seminaire de Probabilités XXXIX, pp. 215-258. Springer, Berlin (2006)
14. Delbaen, F., Peng, S., Rosazza Gianin, E.: Representation of the penalty term of dynamic concave utilities (2008, preprint)
15. Ellsberg D.: Risk, ambiguity and Savage axioms. Quart. J. Econ. 75, 643-669 (1961)
16. de Finetti B.: Sul concetto di media. Giornale dell'Instituto Italiano degli Attuari 2, 369-396 (1931)
17. Föllmer H., Penner I.: Convex risk measures and the dynamics of their penalty functions. Stat. Decis. 24(1), 61-96 (2006)
18. Föllmer, H., Schied, A.: Stochastic Finance. An Introduction in Discrete Time. de Gruyter Studies in Mathematics 27 (2002c)
19. Frittelli M., Rosazza Gianin E.: Law-invariant convex risk measures. Adv. Math. Econ. 7, 33-46 (2005)
20. Gilboa I., Schmeidler D.: Maxmin expected utility with non-unique prior. J. Math. Econ. 18, 141-153 (1989)
21. Gerber H.U.: An Introdution to Mathematical Risk Theory. S.S. Huebner Foundation for Insurance Education, Wharton School, University of Pennsylvania, Philadelphia (1979)
22. Gerber, H.U.: On iterative Premium Calculation Principles. Sonderabdruck aus den Mitteilungen der Vereinigung schweizerischer Versicherungsmathematiker, vol. 74. Band, Heft 2 (1974)
23. Gerber H.U., Goovaerts M.: On the representation of additive principles of premium calculation. Scand. Actuarial J. 4, 221-227 (1981)
24. Goovaerts M., Kaas R., Laeven R., Tang Q.: A comonotonic image of independence for additive risk measures. Insur. Math. Econ. 35, 581-594 (2004)
25. Hardy G., Littlewood J.E., Pólya G.: Inequalities, 2nd edn. Cambridge University press, Cambridge (1952)
26. Jouini, E., Schachermayer, W., Touzi, N.: Law invariant risk measures have the Fatou property. Adv. Math. Econ. 9, 49-71 (2006)
27. Kolmogorov A.N.: Sur la notion de la moyenne. Atti della R. Accademia Nazionale dei Lincei 12, 388-391 (1930)
28. Kusuoka S.: On law-invariant coherent risk measures. Adv. Math. Econ. 3, 83-95 (2001)
29. Machina M.: Dynamic consistency and non-expected utility models of choice under uncertainty. J. Econ. Lit. 27, 1622-1668 (1989)
30. Maccheroni F., Marinacci M., Rustichini A.: Ambiguity aversion, robustness, and the variational representation of preferences. Econometrica 74, 1447-1498 (2006)
31. Nagumo M.: Über eine Klasse der Mittelwerte. Jpn. J. Math. 7, 71-79 (1930)
32. Von Neumann J., Morgenstern O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)
33. Revuz D., Yor M.: Continuous Martingales and Brownian Motion, 2nd edn. Springer, Berlin (1994)
34. Savage L.J.: The Foundations of Statistics. Wiley Publ. Stat., Wiley, New York (1954)
35. Weber S.: Distribution-invariant risk measures, information, and dynamic consistency. Math. Finance 16(2), 419-442 (2006)