Arrow-Debreu equilibria for rank-dependent utilities. (English) Zbl 1348.91204
Summary: We provide conditions on a one-period-two-date pure exchange economy with rank-dependent utility agents under which Arrow-Debreu equilibria exist. When such an equilibrium exists, we show that the state-price density is a weighted marginal rate of intertemporal substitution of a representative agent, where the weight depends on the differential of the probability weighting function. Based on the result, we find that asset prices depend upon agents’ subjective beliefs regarding overall consumption growth, and we offer a direction for possible resolution of the equity premium puzzle.
Keywords:
rank-dependent utility; probability weighting; Arrow-Debreu equilibrium; state-price densityReferences:
| [1] | Abdellaoui, M. (2002): A Genuine Rank‐Dependent Generalization of the Von Neumann‐Morgenstern Expected Utility Theorem, Econometrica70, 717-736. · Zbl 1103.91337 |
| [2] | Azevedo, E. M., and D.Gottlieb (2012): Risk‐Neutral Firms Can Extract Unbounded Profits from Consumers with Prospect Theory Preferences, J. Econ. Theory147, 1291-1299. · Zbl 1258.91125 |
| [3] | Barberis, N., and M.Huang (2008): Stocks as Lotteries: The Implications of Probability Weighting for Security Prices, Am. Econ. Rev.98, 2066-2100. |
| [4] | Carlier, G., and R.‐A.Dana (2006): Law Invariant Concave Utility Functions and Optimization Problems with Monotonicity and Comonotonicity Constraints, Stat. Decis.24, 127-152. · Zbl 1108.49021 |
| [5] | Carlier, G., and R.‐A.Dana (2008): Two‐Person Efficient Risk‐Sharing and Equilibria for Concave Law‐Invariant Utilities, Econ. Theory36, 189-223. · Zbl 1152.91035 |
| [6] | Carlier, G., and R.‐A.Dana (2011): Optimal Demand for Contingent Claims When Agents Have Law Invariant Utilities, Math. Finance21, 169-201. · Zbl 1230.91173 |
| [7] | Dana, R.‐A. (1993a): Existence and Uniqueness of Equilibria When Preferences Are Additively Separable, Econometrica61, 953-957. · Zbl 0784.90013 |
| [8] | Dana, R.‐A. (1993b): Existence, Uniqueness and Determinacy of Arrow‐Debreu Equilibria in Finance Models, J. Math. Econ.22, 563-579. · Zbl 0790.90012 |
| [9] | Dana, R.‐A. (2011): Comonotonicity, Efficient Risk‐Sharing and Equilibria in Markets with Short‐Selling for Concave Law‐Invariant Utilities, J. Math. Econ.47, 328-335. · Zbl 1242.91075 |
| [10] | De Giorgi, E., T.Hens, and M. O.Rieger (2010): Financial Market Equilibria with Cumulative Prospect Theory, J. Math. Econ.46, 633-651. · Zbl 1232.91241 |
| [11] | Dybvig, P. H. (1988): Distributional Analysis of Portfolio Choice, J. Bus.61, 369-398. |
| [12] | Föllmer, H., and A.Schied (2011): Stochastic Finance: An Introduction in Discrete Time, 3rd ed., Berlin: Walter de Gruyter. · Zbl 1213.91006 |
| [13] | He, X. D., and X. Y.Zhou (2011a): Portfolio Choice via Quantiles, Math. Finance21, 203-231. · Zbl 1229.91291 |
| [14] | He, X. D., and X. Y.Zhou (2011b): Portfolio Choice under Cumulative Prospect Theory: An Analytical Treatment, Manage. Sci.57, 315-331. · Zbl 1214.91099 |
| [15] | He, X. D., and X. Y.Zhou (2016): Hope, Fear and Aspirations, Math. Finance26(1), 3-50. · Zbl 1403.91313 |
| [16] | Jin, H., and X. Y.Zhou (2008): Behavioral Portfolio Selection in Continuous Time, Math. Finance18, 385-426. Erratum: Math. Finance 20, 521-525, 2010. · Zbl 1141.91454 |
| [17] | Kahneman, D., and A.Tversky (1979): Prospect Theory: An Analysis of Decision under Risk, Econometrica47, 263-291. · Zbl 0411.90012 |
| [18] | Kramkov, D., and W.Schachermayer (1999): The Asymptotic Elasticity of Utility Functions and Optimal Investment in Incomplete Markets, Ann. Appl. Probab.9, 904-950. · Zbl 0967.91017 |
| [19] | Lopes, L. L. (1987): Between Hope and Fear: The Psychology of Risk, Adv. Exp. Soc. Psychol.20, 255-295. |
| [20] | Lopes, L. L., and G. C.Oden (1999): The Role of Aspiration Level in Risk Choice: A Comparison of Cumulative Prospect Theory and SP/A Theory, J. Math. Psychol. 43(2), 286-313. · Zbl 0946.91024 |
| [21] | Mankiw, N. G., and S. P.Zeldes (1991): The Consumption of Stockholders and Nonstockholders, J. Financ. Econ.29, 97-112. |
| [22] | Mehra, R., and E. C.Prescott (1985): The Equity Premium: A Puzzle, J. Monetary Econ.15, 145-161. |
| [23] | Prelec, D. (1998): The Probability Weighting Function, Econometrica66, 497-527. · Zbl 1009.91007 |
| [24] | Quiggin, J. (1982): A Theory of Anticipated Utility, J. Econ. Behav. Organ.3, 323-343. |
| [25] | Quiggin, J. (1993): Generalized Expected Utility Theory: The Rank‐Dependent Model, Boston: Kluwer. |
| [26] | Schied, A. (2004): On the Neyman‐Pearson Problem for Law‐Invariant Risk Measures and Robust Utility Functionals, Ann. Appl. Probab.14, 1398-1423. · Zbl 1121.91054 |
| [27] | Schmeidler, D. (1989): Subject Probability and Expected Utility without Additivity, Econometrica57, 571-587. · Zbl 0672.90011 |
| [28] | Shefrin, H. (2008): A Behavioral Approach to Asset Pricing, 2nd ed., Amsterdam: Elsevier. |
| [29] | Starmer, C. (2000): Developments in Non‐Expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk, J. Econ. Lit.38, 332-382. |
| [30] | Tversky, A., and D.Kahneman (1992): Advances in Prospect Theory: Cumulative Representation of Uncertainty, J. Risk Uncertainty5, 297-323. · Zbl 0775.90106 |
| [31] | Yaari, M. E. (1987): The Dual Theory of Choice under Risk, Econometrica55, 95-115. · Zbl 0616.90005 |
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