2007 | OriginalPaper | Buchkapitel
On the Smooth-Fit Property for One-Dimensional Optimal Switching Problem
verfasst von : Huyen Pham
Erschienen in: Séminaire de Probabilités XL
Verlag: Springer Berlin Heidelberg
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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
C
1 property of the value functions. MSC Classification (2000): 60G40, 49L25, 60H30 Key words: Optimal switching, System of variational inequalities, Viscosity solutions, Smooth-fit principle