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SOLUTIONS AND DIAGNOSTICS OF SWITCHING PROBLEMS WITH LINEAR STATE DYNAMICS

Published online by Cambridge University Press:  28 January 2016

J. HINZ*
Affiliation:
School of Mathematical and Physical Sciences, University of Technology Sydney, PO Box 123, Broadway, NSW 2007, Australia email [email protected]
N. YAP
Affiliation:
Finance Discipline Group, UTS Business School, University of Technology Sydney, PO Box 123, Broadway, NSW 2007, Australia email [email protected]
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Abstract

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Optimal control problems of stochastic switching type appear frequently when making decisions under uncertainty and are notoriously challenging from a computational viewpoint. Although numerous approaches have been suggested in the literature to tackle them, typical real-world applications are inherently high dimensional and usually drive common algorithms to their computational limits. Furthermore, even when numerical approximations of the optimal strategy are obtained, practitioners must apply time-consuming and unreliable Monte Carlo simulations to assess their quality. In this paper, we show how one can overcome both difficulties for a specific class of discrete-time stochastic control problems. A simple and efficient algorithm which yields approximate numerical solutions is presented and methods to perform diagnostics are provided.

Type
Research Article
Copyright
© 2016 Australian Mathematical Society 

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