This paper studies the problem of optimal switching for a one-dimensional diffusion, which may be regarded as a sequential optimal stopping problem with changes of regimes. The resulting dynamic programming principle leads to a system of variational inequalities, and the state space is divided into continuation regions and switching regions. By a viscosity solutions approach, we prove the smooth-fit C1 property of the value functions. MSC Classification (2000): 60G40, 49L25, 60H30 Key words: Optimal switching, System of variational inequalities, Viscosity solutions, Smooth-fit principle
Keywords
- Variational Inequality
- Viscosity Solution
- Switching Cost
- Switching Control
- Switching Region
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© 2007 Springer-VerlagBerlinHeidelberg
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Pham, H. (2007). On the Smooth-Fit Property for One-Dimensional Optimal Switching Problem. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, C. (eds) Séminaire de Probabilités XL. Lecture Notes in Mathematics, vol 1899. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71189-6_8
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DOI: https://doi.org/10.1007/978-3-540-71189-6_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71188-9
Online ISBN: 978-3-540-71189-6
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