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Dynamic programming for discrete-time finite-horizon optimal switching problems with negative switching costs

Part of: Applications Stochastic systems and control Stochastic processes

Published online by Cambridge University Press:  19 September 2016

R. Martyr
R. Martyr*
Affiliation:
The University of Manchester
*
* Current address: School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK. Email address: [email protected]
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Abstract

In this paper we study a discrete-time optimal switching problem on a finite horizon. The underlying model has a running reward, terminal reward, and signed (positive and negative) switching costs. Using optimal stopping theory for discrete-parameter stochastic processes, we extend a well-known explicit dynamic programming method for computing the value function and the optimal strategy to the case of signed switching costs.

Keywords

Optimal switchingstopping timeoptimal stopping problemSnell envelope

MSC classification

Primary: 93E20: Optimal stochastic control
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 62P20: Applications to economics
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 3 , September 2016 , pp. 832 - 847
Copyright
Copyright © Applied Probability Trust 2016 

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References

[1] Carmona, R. and Ludkovski, M. (2008).Pricing asset scheduling flexibility using optimal switching.Appl. Math. Finance 15,405–447.CrossRefGoogle Scholar
[2] Djehiche, B.,Hamadène, S. and Popier, A. (2009).A finite horizon optimal multiple switching problem.SIAM J. Control Optimization 48,2751–2770.CrossRefGoogle Scholar
[3] Gassiat, P.,Kharroubi, I. and Pham, H. (2012).Time discretization and quantization methods for optimal multiple switching problem.Stoch. Process. Appl. 122,2019–2052.Google Scholar
[4] Guo, X. and Tomecek, P. (2008).Connections between singular control and optimal switching.SIAM J. Control Optimization 47,421–443.Google Scholar
[5] Kunita, H. and Seko, S. (2004).Game call options and their exercise regions. Tech. Rep., Nanzan Academic Society, Mathematical Sciences and Information Engineering.Google Scholar
[6] Martyr, R. (2016).Solving finite time horizon Dynkin games by optimal switching. To appear in J. Appl. Prob. Google Scholar
[7] Peskir, G. and Shiryaev, A. (2006).Optimal Stopping and Free-Boundary Problems.Birkhäuser,Basel.Google Scholar
[8] Rogers, L. C. G. and Williams, D. (2000).Diffusions, Markov Processes, and Martingales, Vol. 1, Foundations.Cambridge University Press.Google Scholar
[9] Tanaka, T. (1990).Two-parameter optimal stopping problem with switching costs.Stoch. Process. Appl. 36,153–163.Google Scholar
[10] Yushkevich, A. and Gordienko, E. (2002).Average optimal switching of a Markov chain with a Borel state space.Math. Meth. Operat. Res. 55,143–159.Google Scholar