Optimal risk sharing for law invariant monetary utility functions

Mathematical Finance

Volumn 18, Issue 2, 2008, Pages 269-292

  Jouini, E ^a   Schachermayer, W ^b   Touzi, N ^c  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^c ECOLE POLYTECHNIQUE   (France)

Author keywords

Comonotonicity; Monetary utility functions; Pareto optimal allocations

Indexed keywords

EID: 34548595043     PISSN: 09601627     EISSN: 14679965     Source Type: Journal    
DOI: 10.1111/j.1467-9965.2007.00332.x     Document Type: Article

References (36)

1. Arrow, K. J. (1963): Uncertainty and the Welfare of Medical Care, Am. Econ. Rev. 53, 941–973.
2. Artzner, P., F. Delbaen, J. M. Eber, and D. Heath (1999): Coherent Measures of Risk, Math. Finance 9, 203–228.
3. Barrieu, P., and N. El Karoui (2002a): Reinsuring climatic risk using optimally designed weather bonds, Geneva Papers, Risk and Insurance Theory 27, 87–113.
4. Barrieu, P., and N. El Karoui (2002b): Optimal Design of Derivatives in Illiquid Markets, Quant. Finance 2, 1–8.
5. Barrieu, P., and N. El Karoui (2004): Optimal Risk Transfer, Finance 25, 31–47.
6. Barrieu, P., and N. El Karoui (2005): Inf‐Convolution of Risk Measures and Optimal Risk Transfer, Finance Stochast. 9, 269–298.
7. Bühlmann, H. (1984): The General Economic Principle Premium, Astin Bull. 14, 13–21.
8. Bühlmann, H., and S. Jewell (1979): Optimal Risk Exchanges, Astin Bull. 10, 243–262.
9. Borch, K. (1962): Equilibrium in a Reinsurance Market, Econometrica 30, 424–444.
10. Brézis, H. (1983): Analyse Fonctionelle. Paris, New York: Masson.
11. Camerer, C. (2003): Behavioral Game Theory. Princeton, NJ: Princeton University Press.
12. Carlier, G., and R.‐A. Dana (2003): Core of Convex Distortions of Probability, J. Econ. Theory 113, 199–222.
13. Dana, R.‐A., and M. Jeanblanc (2003): Financial Markets in Continuous Time. Berlin, Heidelberg, New York: Springer.
14. Dana, R.‐A., and I. Meilijson (2003): Modelling Agents' Preferences in Complete Markets by Second Order Stochastic Dominance, Cahler du Cere made 0333.
15. Dana, R.‐A., and M. Scarsini (2005): Optimal Risk Sharing with Background Risk, J. Econ. Theory 133, 152–176.
16. Denneberg, D. (1994): Non‐Additive Measures and Integrals. Dordrecht, Holland: Kluwer Academic Publishers.
17. Dhaene, J., M. Denuit, M. J. Goovaerts, R. Kaas, and D. Vyncke (2002): The Concept of Comonotonicity in Actuarial Science and Finance: Theory, Insurance: Math. Econ. 31, 3–33.
18. Delbaen, F. (2000): Coherent Risk Measures, Lecture Notes of Scuola Normale, Pisa.
19. Delbaen, F. (2002): Coherent Measures of Risk on General Probability Spaces, in Advances in Finance and Stochastics, Essays in Honor of Dieter Sondermann, ( K. Sandmann and P. J. Schonbucher, eds.) Berlin: Springer, 1–37.
20. Delbaen, F. (2005): Hedging Bounded Claims with Bounded Outcomes, in Advances in Mathematical Economics 8, S. Kusuoka and A. Yamazaki, eds. Springer, 75–86.
21. Frittelli, M., and E. R. Rossaza‐Gianin (2002): Putting Order in Risk Measures, J. Banking Finance 26 (7), 1473–1486.
22. Frittelli, M., and E. R. Rossaza‐Gianin (2005): Law Invariant Convex Risk Measures, Adv. Math. Econ. 7, 33–46.
23. Fischer, T. (2001): Examples of Coherent Risk Measures Depending on One‐Sided Moments, Working paper.
24. Föllmer, H., and A. Schied (2002): Convex Measures of Risk and Trading Constraints, Finance Stochast. 6, 429–448.
25. Föllmer, H., and A. Schied (2004): Stochastic Finance, Second edn. Berlin: de Gruyter.
26. Gerber, H. U. (1979): An Introduction to Mathematical Risk Theory. Huebner Foundation Monograph 8, Wharton School, University of Pennsylvania.
27. Heath, D., and H. Ku (2004): Pareto Equilibria with Coherent Measures of Risk, Math. Finance 14 (2), 163–172.
28. Jouini, E., and C. Napp (2005): Conditional Comonotonicity, Decisions Econ. Finance 27, 153–166.
29. Jouini, E., W. Schachermayer, and N. Touzi (2006): Law‐Invariant Risk Measures Have the Fatou Property, Adv. Math. Economics 9, 49–71.
30. Joseph, H., R. Boyd, S. Bowles, C. Camerer, H. Gintis, R. McElreath, and E. Fehr (2001): In Search of Homo Economicus: Experiments on 15 Small‐Scale Societies, Am. Econ. Rev. 91, 73–79.
31. Klöppel, S., and M. Schweizer (2007): Dynamic Utility Indifference Valuation via Convex Risk Measures, Math. Finance 17, 599–627.
32. Kusuoka, S. (2001): On Law‐Invariant Coherent Risk Measures, Adv. Math. Econ. 3, 83–95.
33. Landsberger, M., and I. Meilijson (1994): Comonotone Allocations, Bickel‐Lehmann Dispersion and the Arrow‐Pratt Measure of Risk Aversion, Ann. Operat. Res. 52, 97–106.
34. Moreau, J. J. Fonctionnelles Convexes (1966): Séminaire Equations aux dérivées partielles. Collége de France.
35. Nowak, M. A., K. Page, and K. Sigmund (2000): Fairness versus Reason in the Ultimatum Game, Science 289, 1773–1775.
36. Rockafellar, R. T. (1997): Convex Analysis, Princeton Landmarks in Mathematics. Princeton, NJ: Princeton University Press.