Abstract
In 2003 Daniel Kahneman won the Nobel Prize for Economics for numerous important contributions. Probably the study with the greatest impact on economic research is his joint contribution with Amos Tversky, called Prospect Theory (PT) and its latest modified version called Cumulative Prospect Theory (CPT). The impact of PT on academic research is tremendous. It helps us to understand people choices in economics, finance, medicine and many more areas. Moreover, it helps explaining people’s behavior and choices in situations where classic expected utility and traditional models fail.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
See, Kahneman, D. and A. Tversky, “Prospect Theory : An Analysis of Decision Under Risk ,” Econometrica, 47, 1979, pp. 263–291 and Tversky A. and D. Kahneman, “Advances In Prospect Theory: Cumulative Representation of Uncertainty ,” Journal of Risk and Uncertainty, 5, 1992, pp. 297–323.
- 2.
The proof, like the proofs of the SD criteria, holds also for the unbounded case, see Hanoch G. and Levy H., “The Efficiency Analysis of Choices Involving Risk ,” Review of Economic Studies, 36, 1969, pp. 335–346.
- 3.
See Chap. 15.
- 4.
For a proof of this claim, see Levy, H., and Z. Wiener, “Stochastic Dominance and Prospect Dominance with Subjective Weighting Functions,” Journal of Risk Uncertainty , 16, 1998, pp. 147–163.
- 5.
See Markowitz, H.M., “The Utility of Wealth,” Journal of Political Economy, 1952, pp. 151–158.
- 6.
The proof of MSD relies on the proof given in Levy, M. and Levy, H., “Prospect Theory : Much Ado About Nothing?,” Management Science, 48, 2002, pp. 1334–1349.
- 7.
Levy, H., and Levy, M., “Prospect Theory and Mean-Variance Analysis,” Review of Economic Studies, 17, 2004, pp. 1015–1041.
- 8.
Levy, H., E. DeGiorgi, and T. Hens., “Two Paradigms and Two Nobel Prizes in Economics: A Contradiction or Coexistence?,” European Financial management, 2012, 18, pp. 162–182.
- 9.
DeGiorgi, E., T. Hens and Levy, H., “Existence of CAPM Equilibria with Prospect Theory Preferences,” working paper, 2003.
- 10.
Levy, M., H. Levy, “Testing for risk aversion : A stochastic dominance approach,” Economic Letters, 71, 2001, pp. 233–240.
- 11.
Battalio, R.C., Kagel, J.H., and Jiranyakul, K., “Testing between alternative models of choice under uncertainty : some initial results.” Journal of Risk and Uncertainty , 3, 1990, pp. 25–50.
- 12.
Tversky, A., & Kahneman, D. “The framing of decisions and the psychology of choice,” Science, 211, 1981, pp. 453–458.
- 13.
Schneider, S.L., & Lopes, L.L., “Reflection in preferences under risk : Who and when may suggest why,” Journal of Experimental Psychology: Human Perception and Performance, 1986, 12, pp. 535–548.
- 14.
See footnote 10.
- 15.
Levy, H., and Levy, M., “Experimental test of the prospect theory value function : A stochastic dominance approach,” Organizational Behavior and Human Decision Processes, 2002, 89, pp. 1058–1081.
- 16.
Notice that for mixed prospects the decision weight s do not generally add up to 1 (Tversky & Kahneman, 1992, p. 301). In Task II, the decision weights add up to .875 for F and to .866 for G. We assign the probability which is “missing” to the outcome 0, which of course does not affect the results by CPT V(0) = 0. If all outcomes are either positive or negative we obtain by CPT that Σ. w(p) = 1. In such cases, experimental findings strongly reject CPT.
- 17.
For the importance of skewness see Levy, H., “A utility function depending on the first three moments,” Journal of Finance, 1969, 24, pp. 715–719, Arditti, F.D., “Risk and the Required Return on Equity,” Journal of Finance, 1967, 22, pp. 19–36, Kraus, A. and R.H. Litzenberger, “Skewness Preferences and the valuation of risk assets,” Journal of Finance, 1976, 31, pp. 1085–1100, and Harvey, C., and A. Siddique, “Conditional Skewness in asset pricing tests,” Journal of Finance, 2000, 55, pp. 1263–1295.
- 18.
Post, Thierry, “Empirical test for stochastic dominance efficiency,” Journal of Finance, 2003, 58, pp. 1905–1932.
- 19.
There are several working papers on this issue. Yitzhaki and Mayshar follow a distributional approach to SSD while Post employs necessary and sufficient utility function restriction. Both methods reduce to a linear programming problem. Bodurtha develops algorithms that efficiently identify improvements to dominated choices or preference functions choosing undominated choices. For more details on works dealing with this issue, see: Yitzhaki, S., and J. Mayshar, “Characterizing Efficient Portfolios,” Hebrew University of Jerusalem, 1997, working paper, Kuosmanen, T., “Efficient Diversification According to Stochastic Dominance Criteria,” Management Science, 2005, 50, pp. 1390–1406, and Bodurtha, J.N., “Second-Order Dominance Dominated, Undominated and Optimal Portfolio s,” Georgetown University, 2003, working paper.
- 20.
Post, Thierry, and Pim Van Vliet. “Downside risk and asset pricing,” Journal of Banking & Finance, 2006, 30, pp. 823–849.
- 21.
Post, T. and Levy, H., “Does Risk Seeking Drive Stock Prices,” Review of Financial and Studies, 2005, 18, pp. 925–953.
- 22.
Fama, E.F., and K.R. French, “The cross-section of expected stock returns,” Journal of Finance, 1992, 47, pp. 427–465.
- 23.
Carhart, M.M., R.J. Krail, R.J. Stevens and K.E. Welch, “Testing the conditional CAPM ,” 1996, unpublished manuscript, University of Chicago.
- 24.
Carhart, M.M., “On persistence in mutual fund performance,” Journal of Finance, 1997, 52, pp. 57–82.
References
Lintner, J., "Security Prices, Risk, and Maximal Gains from Diversification." The Journal of Finance, 20, 1965, 587–615.
Sharpe, W.F., “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk,” Journal of Finance, 19, 1964, 425–442.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Levy, H. (2016). Stochastic Dominance and Prospect Theory. In: Stochastic Dominance. Springer, Cham. https://doi.org/10.1007/978-3-319-21708-6_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-21708-6_16
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21707-9
Online ISBN: 978-3-319-21708-6
eBook Packages: Economics and FinanceEconomics and Finance (R0)