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An Optimal Stopping Problem Arising from a Decision Model with Many Agents

Published online by Cambridge University Press:  27 July 2009

Bruno Bassan  and
Claudia Ceci
Bruno Bassan
Affiliation:
Dipartimento di Matematica, Università “La Sapienza”, 1-00185 Roma, Italy
Claudia Ceci
Affiliation:
Dipartimento di Scienze, Università G. D'Annunzio, 1-65127 Pescara, Italy
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Abstract

We study an optimal stopping problem for a nonhomogeneous Markov process, with a reward function that is lower semicontinuous everywhere and smooth in certain regions. We prove that the payoff (value function) is lower semicontinuous as well and solves a so-called generalized Stefan problem in each of these regions. We provide some results for the geometry of the “stopping observations” set. Our results generalize those in Bassan, Brezzi, and Scarsini (1996). The problem we consider stems from an economic model in which several self-interested agents desire information, whereas a social planner, although benevolent toward the agents, might decide to withhold information in order to induce diversification in their behavior.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 12 , Issue 3 , July 1998 , pp. 393 - 408
Copyright
Copyright © Cambridge University Press 1998

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References

1.Bassan, B., Brezzi, M., & Scarsini, M. (1996). Information in continuous time decision models with many agents. Probability in the Engineering and Informational Sciences 10: 543–555.CrossRefGoogle Scholar
2.Bassan, B. & Scarsini, M. (1995). On the value of information in multi-agent decision theory. Journal of Mathematical Economics 24: 557–576.CrossRefGoogle Scholar
3.Bassan, B. & Scarsini, M. (1996). The social value of withholding information. Rivista Internationale di Scienze Economiche e Commerciali 43: 267–277.Google Scholar
4.Bassan, B. & Scarsini, M. (1998). Sequential decisions with several agents. Economic Theory (to appear).CrossRefGoogle Scholar
5.Bensoussan, A. & Lions, J.L. (1978). Applications des inéquations variationelles en contrôle stochastique. Paris: Dunod.Google Scholar
6.Bismut, J.M. & Skalli, B. (1977). Temps d'arrêt optimal, théorie générale des processus et processus de Markov. Zeitschrift für Warscheinlicheitsrechnung und Verwande Gebiete 39: 301–313.CrossRefGoogle Scholar
7.Blackwell, D. & Dubins, L. (1962). Merging of opinions with increasing information. Annals of Mathematical Statistics 38: 882–886.CrossRefGoogle Scholar
8.Dynkin, E.B. (1965). Markov processes. New York: Springer-Verlag.Google Scholar
9.El Karoui, N. (1981). Les aspects probabilistes du contrôle stochastique. Ecole d'été de Saint-Flour 1979. New York: Springer-Verlag.CrossRefGoogle Scholar
10.Ethier, S.N. & Kurtz, T.G. (1986). Markov processes: Characterization and convergence. New York: John Wiley & Sons.CrossRefGoogle Scholar
11.Gihman, I.I. & Skorohod, A.V. (1972). Stochastic differential equations. New York: Springer-Verlag.CrossRefGoogle Scholar
12.Liptser, R. & Shiryayev, A. (1977). Statistics of random processes, I. New York: Springer-Verlag.CrossRefGoogle Scholar
13.Menaldi, J.L. (1980). On the optimal stopping time problem for degenerate diffusions. SIAM Journal of Control and Optimization 18: 697–721.CrossRefGoogle Scholar
14.Sharpe, M. (1988). General theory of Markov processes. New York: Academic Press.Google Scholar
15.Shiryayev, A. (1978). Optimal stopping rules. New York: Springer-Verlag.Google Scholar