Lebesgue property for convex risk measures on Orlicz spaces

Mathematics and Financial Economics - Tập 6 Số 1 - Trang 15-35 - 2012
J. Orihuela1, M. Ruiz Galán2
1Universidad de Múrcia
2Dpto. Matemática Aplicada, Universidad de Granada, E.T.S. Ingeniería de Edificación, Granada, Spain

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Tài liệu tham khảo

Bourgain, J.: La propiété de Radon-Nikodým Publications Mathématiques de l’Université Pierre et Marie Curie. 36 (1979)

Biagini, S., Fritelli, M.: On the Extension of the Namioka-Klee Theorem and on the Fatou Property for Risk Measures Optimality and Risk- Modern Trends in Mathematical Finance. The Kabanov Festschrift, pp. 1–28. Springer, Berling (2009)

Biagini S., Fritelli M.: A unified framework for utility maximization problems: an Orlicz space approach. Ann. Appl. Prob. 18(3), 929–966 (2008)

Calvert B., Fitzpatrick S.: Erratum: In a nonreflexive space the subdifferential is not onto. Math. Z. 235, 627 (2000)

Cascales B., Fonf V., Orihuela J., Troyanski S.: Boundaries of Asplund spaces. J. Funct. Anal. 259, 1346–1368 (2010)

Cheridito P., Li T.: Risks measures on Orlicz hearts. Math. Financ. 19(2), 189–214 (2009)

Delbaen F. : Differentiability properties of utility functions. In: Delbaen, F. et al. (eds) Optimality and Risk-Modern Trends in Mathematical Finance, pp. 39–48. Springer, Berlin (2009)

Delbaen F.: Coherent Risk Measures. Cattedra Galileiana, Scuola Normale Superiore Pisa (2003)

Delbaen, F.: Draft: monetary utility functions. Lectures notes in preparation. Personal communication

Diestel J.: Sequences and Series in Banach Spaces. GTM 92 Springer Verlag, New York (1984)

Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V.: Banach Space Theory. The Basis for Linear and Nonlinear Analysis. Springer, CMS Books in Mathematics, Berlin (2011)

Föllmer, H., Schied, A.: Stochastic Finance. An Introduction in Discrete Time de Gruyter Studies in Mathematics 27, 2nd edn. Walter de Gruyter, Berlin (2004)

Haydon R., Levy M., Odell E.: On sequences without weak* convergent convex block subsequences. Proc. Am. Math. Soc. 100, 94–98 (1987)

James R.C.: Reflexivity and the sup of linear functionals. Isr. J. Math. 13, 289–300 (1972)

Jouini E., Schachermayer W., Touzi N.: Law invariant risk measures have the Fatou property. Adv. Math. Econ. 9, 49–71 (2006)

Orihuela J., Ruiz Galán M.: A coercive James’s weak compactness theorem and nonlinear variational problems. Nonlinear Anal. 75, 598–611 (2012)

Pták, V.: A combinatorial lemma on the existence of convex means and its applications to weak compactness. In: Klee, V. (ed.) Proceedings of symposia in pure mathematics VII, convexity. American Mathematical Society, Providence, (1963)

Rao M.M., Ren Z.D.: Theory of Orlicz Spaces. Marce Dekker, Inc, Ney York (1991)

Ruiz Galán M., Simons S.: A new minimax theorem and a perturbed James’s theorem. Bull. Austr. Math. Soc. 66, 43–56 (2002)

Saint Raymond, J.: Characterizing convex functions on a reflexive Banach space (preprint)

Simons S.: An eigenvector proof of Fatou’s lemma for continuous functions. Math. Intell. 17, 67–70 (1995)

Simons, S.: From Hahn-Banach to Monotonicity. Lecture Notes in Mathematicas 1693. Springer Verlag, New York (2008)