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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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