Optimal Stopping with Information Constraint

Optimal Stopping with Information Constraint 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Optimal Stopping with Information Constraint

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Publisher
Springer-Verlag
Copyright
Copyright © 2012 by Springer Science+Business Media, LLC
Subject
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-012-9166-0
Publisher site
See Article on Publisher Site

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.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2012

References

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