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SOLUTIONS AND DIAGNOSTICS OF SWITCHING PROBLEMS WITH LINEAR STATE DYNAMICS

Part of: Mathematical finance Numerical methods in calculus of variations and optimal control

Published online by Cambridge University Press:  28 January 2016

J. HINZ  and
N. YAP
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]
*
✉[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.

Keywords

Markov decisionsapproximate dynamic programmingstochastic controlduality

MSC classification

Primary: 49M29: Methods involving duality
Secondary: 49M25: Discrete approximations 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems) 90C39: Dynamic programming
Type
Research Article
Information
The ANZIAM Journal , Volume 57 , Issue 3 , January 2016 , pp. 339 - 351
Copyright
© 2016 Australian Mathematical Society 

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