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Optimal Stopping with Information Constraint

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Abstract

We study the optimal stopping problem proposed by Dupuis and Wang (Adv. Appl. Probab. 34:141–157, 2002). In this maximization problem of the expected present value of the exercise payoff, the underlying dynamics follow a linear diffusion. The decision maker is not allowed to stop at any time she chooses but rather on the jump times of an independent Poisson process. Dupuis and Wang (Adv. Appl. Probab. 34:141–157, 2002), solve this problem in the case where the underlying is a geometric Brownian motion and the payoff function is of American call option type. In the current study, we propose a mild set of conditions (covering the setup of Dupuis and Wang in Adv. Appl. Probab. 34:141–157, 2002) on both the underlying and the payoff and build and use a Markovian apparatus based on the Bellman principle of optimality to solve the problem under these conditions. We also discuss the interpretation of this model as optimal timing of an irreversible investment decision under an exogenous information constraint.

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Acknowledgements

An anonymous referee is gratefully acknowledged for careful reading and for a number of very helpful comments. The author thanks Prof. Luis H.R. Alvarez, Prof. Fred Espen Benth, Dr. Paul C. Kettler, Prof. Andreas E. Kyprianou and Prof. Paavo Salminen for discussions and comments on earlier versions of this paper. Financial support from Research Foundation of OP-Pohjola group and the project “Electricity markets: modelling, optimization and simulation (EMMOS)” funded by the Norwegian Research Council under grant 205328/v30 is acknowledged. Prof. Esko Valkeila and Department of Mathematics and System Analysis in Aalto University School of Science and Technology are acknowledged for hospitality.

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  1. Centre of Mathematics for Applications, University of Oslo, PO Box 1053, Blindern, 0316, Oslo, Norway

    Jukka Lempa

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Lempa, J. Optimal Stopping with Information Constraint. Appl Math Optim 66, 147–173 (2012). https://doi.org/10.1007/s00245-012-9166-0

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