Randomized strategies and prospect theory in a dynamic context. (English) Zbl 1400.91178
Summary: When prospect theory (PT) is applied in a dynamic context, the probability weighting component brings new challenges. We study PT agents facing optimal timing decisions and consider the impact of allowing them to follow randomized strategies. In a continuous-time model of gambling and optimal stopping, S. Ebert and P. Strack [“Until the bitter end: on prospect theory in a dynamic context”, Am. Econ. Rev., 105, No. 4, 1618–1633 (2015; doi:10.1257/aer.20130896)] show that a naive PT investor with access only to pure strategies never stops. We show that allowing randomization can significantly alter the predictions of their model, and can result in voluntary cessation of gambling.
References:
| [1] | Azéma, J.; Yor, M., Une solution simple au problème de Skorokhod, (Séminaire de Probabilités, XIII. Séminaire de Probabilités, XIII, Lecture Notes in Math., vol. 721 (1979), Springer: Springer Berlin), 90-115, 625-633 · Zbl 0414.60055 |
| [2] | Azevedo, E.; Gottlieb, D., Risk neutral firms can extract unbounded profits from consumers with prospect theory preferences, J. Econ. Theory, 147, 1291-1299 (2012) · Zbl 1258.91125 |
| [3] | Agranov, M.; Ortoleva, P., Stochastic choice and preferences for randomization, J. Polit. Econ (2015), forthcoming |
| [4] | Barberis, N., A model of casino gambling, Manag. Sci., 58, 35-51 (2012) |
| [5] | Bertoin, J.; Le Jan, Y., Representation of measures by balayage from a regular recurrent point, Ann. Probab., 20, 1, 538-548 (1992) · Zbl 0749.60038 |
| [6] | Carassus, L.; Rásonyi, M., On optimal investment for behavioral investors in discrete-time multiperiod incomplete markets, Math. Finance, 25, 115-153 (2015) · Zbl 1318.91176 |
| [7] | Chateauneuf, A.; Eichberger, J.; Grant, S., Choice under uncertainty with the best and worst in mind: NEO-additive capacities, J. Econ. Theory, 137, 538-567 (2007) · Zbl 1132.91420 |
| [8] | Ebert, S.; Strack, P., Until the bitter end: on prospect theory in a dynamic context, Am. Econ. Rev., 105, 4, 1618-1633 (2015) |
| [9] | Goldstein, W. M.; Einhorn, H. J., Expression theory and the preference reversal phenomena, Psychol. Rev., 94, 236-254 (1987) |
| [10] | He, X. D.; Hu, S.; Oblòj, J.; Zhou, X. Y., Technical note - Path-dependent and randomized strategies in Barberis’ casino gambling model, Oper. Res (2016), Published online in Articles in Advance 01 Nov. 2016 |
| [11] | Kahneman, D.; Tversky, A., Prospect theory: an analysis of decision under risk, Econometrica, 46, 171-185 (1979) |
| [12] | Köbberling, V.; Wakker, P. P., An index of loss aversion, J. Econ. Theory, 122, 119-131 (2005) · Zbl 1118.91057 |
| [13] | Kothiyal, A.; Spinu, V.; Wakker, P. P., Prospect theory for continuous distributions: a preference foundation, J. Risk Uncertain., 42, 195-210 (2011) · Zbl 1214.91032 |
| [14] | Machina, M., Dynamic consistency and non-expected utility models of choice under uncertainty, J. Econ. Lit., 27, 1622-1668 (1989) |
| [15] | Quiggin, J., A theory of anticipated utility, J. Econ. Behav. Organ., 3, 323-343 (1982) |
| [16] | Tversky, A.; Kahneman, D., Advances in prospect theory: cumulative representation of uncertainty, J. Risk Uncertain., 5, 297-323 (1992) · Zbl 0775.90106 |
| [17] | Wakker, P., Separating marginal utility and probabilistic risk aversion, Theory Decis., 36, 1, 1-44 (1994) · Zbl 0812.90010 |
| [18] | Wakker, P., Prospect Theory for Risk and Ambiguity (2010), Cambridge University Press · Zbl 1200.91004 |
| [19] | Webb, C. S., Piecewise additivity for non-expected utility, Econ. Theory, 60, 2, 371-392 (2015) · Zbl 1367.91068 |
| [20] | Xu, Z.; Zhou, X. Y., Optimal stopping under probability distortion, Ann. Appl. Probab., 23, 1, 251-282 (2013) · Zbl 1286.60038 |
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