Giammarino, Flavia and Barrieu, Pauline (2011): Indifference pricing with uncertainty averse preferences.
Download (182kB) | Preview
We consider the indifference valuation of an uncertain monetary payoff from the perspective of an uncertainty averse decision maker. We study how the indifference valuation depends on the decision maker’s attitudes toward uncertainty. We obtain a characterization of comparative uncertainty aversion and various characterizations of increasing, decreasing, and constant uncertainty aversion.
|Item Type:||MPRA Paper|
|Original Title:||Indifference pricing with uncertainty averse preferences|
|Keywords:||Indifference Pricing; Uncertainty Aversion; Risk Measures; Quasiconvexity; Cash-Subadditivity|
|Subjects:||D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty
G - Financial Economics > G2 - Financial Institutions and Services > G22 - Insurance; Insurance Companies
C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods
D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D52 - Incomplete Markets
D - Microeconomics > D0 - General > D01 - Microeconomic Behavior: Underlying Principles
|Depositing User:||Flavia Giammarino|
|Date Deposited:||14. Aug 2012 01:46|
|Last Modified:||15. Feb 2013 23:02|
F. J. Anscombe and R. J. Aumann. A Definition of Subjective Probability. The Annals of Mathematical Statistics, 34(1):199–205, 1963.
K. J. Arrow. Essays in the Theory of Risk Bearing. North-Holland, 1970.
P. Artzner, F. Delbaen, J. M. Eber, and D. Heath. Thinking Coherently. Risk, 10:68–71, 1997.
P. Artzner, F. Delbaen, J. M. Eber, and D. Heath. Coherent Measures of Risk. Mathematical Finance, 9(3):203–228, 1999.
D. Bernoulli. Exposition of a New Theory on the Measurement of Risk. Econometrica, 22(1):23–36, 1954. Translated from Latin into English by Dr. Louise Sommer from “Specimen Theoriae Novae de Mensura Sortis”, Commentarii Academiae Scientiarum Imperialis Petropolitanae, Tomus V, Papers of the Imperial Academy of Sciences in Petersburg, Vol. V, 1738, pp. 175–192.
S. Cerreia Vioglio, F. Maccheroni, M. Marinacci, and L. Montrucchio. Uncertainty Averse Preferences. Journal of Economic Theory, 146(4):1275–1330, 2011a.
S. Cerreia Vioglio, F. Maccheroni, M. Marinacci, and L. Montrucchio. Risk Measures: Rationality and Diversification. Mathematical Finance, 21(4):743–774, 2011b.
B. de Finetti. Foresight: Its Logical Laws, Its Subjective Sources. In H. E. Kyburg and H. E. Smokler, editors, Studies in Subjective Probability, pages 93–158. Wiley, 1964. Translated from French into English by Prof Henry E. Kyburg, from “La Pr´evision, ses Lois Logiques, ses Sources Subjectives”, Annales de l’Institut Henri Poincare, Tome 7, No. 1, 1937, pp. 1-68.
B. de Finetti. Sulla preferibilita. Giornale degli Economisti e Annali di Economia, XI: 685–709, 1952.
O. Deprez and H. U. Gerber. On Convex Principles of Premium Calculation. Insurance: Mathematics and Economics, 4:179 – 189, 1985.
S. Drapeau and M. Kupper. Risk Preferences and their Robust Representation. Preprint, May 2010.
N. El Karoui and C. Ravanelli. Cash Sub-Additive Risk Measures and Interest Rate Ambiguity. Mathematical Finance, 19(4):561–590, 2009.
H. Follmer and A. Schied. Convex Measures of Risk and Trading Constraints. Finance and Stochastics, 6:429–447, 2002.
H. Follmer and A. Schied. Stochastic Finance. An Introduction in Discrete Time. De Gruyter Studies in Mathematics, Second edition, 2004.
M. Frittelli and M. Maggis. Dual Representation of Quasiconvex Conditional Maps. SIAM Journal on Financial Mathematics, 2:357–382, 2011a.
M. Frittelli and M. Maggis. Conditional Certainty Equivalent. International Journal of Theoretical and Applied Finance, 14(1):41–59, 2011b.
M. Frittelli and E. Rosazza Gianin. Putting Order in Risk Measures. Journal of Banking & Finance, 26:1473–1486, 2002.
P. Ghirardato and M. Marinacci. Ambiguity Made Precise: A Comparative Foundation. Journal of Economic Theory, 102:251 – 289, 2001.
F. Giammarino. Indifference Pricing with Uncertainty Averse Preferences. PhD thesis, London School of Economics and Political Science (LSE), 2011.
I. Gilboa and D. Schmeidler. Maxmin Expected Utility with Non-Unique Prior. Journal of Mathematical Economics, 18(2):141 – 153, 1989.
D. M. Kreps. Notes on the Theory of Choice. Westview Press, 1988.
F. Maccheroni, M. Marinacci, and A. Rustichini. Ambiguity Aversion, Robustness, and the Variational Representation of Preferences. Econometrica, 74(6):1447–1498, 2006.
J. W. Pratt. Risk Aversion in the Small and in the Large. Econometrica, 32 (1/2):122–136, 1964.
F. P. Ramsey. Truth and Probability. In The Foundations of Mathematics and Other Logical Essays, pages 62–92. Routledge & Kegan Paul, 1931.
R. T. Rockafellar. Convex Analysis. Princeton University Press, 1970.
L. J. Savage. The Foundations of Statistics. Dover, Second edition, 1972.
J. von Neumann and O. Morgenstern. Theory of Games and Economic Behaviour. Princeton University Press, Third edition, 1953.
M. E. Yaari. Some Remarks on Measures of Risk Aversion and on Their Uses. Journal of Economic Theory, 1(3):315 – 329, 1969.