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A stochastic target formulation for optimal switching problems in finite horizon

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Date
2009-09-24
Dewey
Probabilités et mathématiques appliquées
Sujet
Viscosity solutions; Optimal Control
Journal issue
Stochastics
Volume
81
Number
2
Publication date
04-2009
Article pages
171 - 197
Publisher
Taylor & Francis
DOI
http://dx.doi.org/10.1080/17442500802327360
URI
https://basepub.dauphine.fr/handle/123456789/1933
Collections
  • CEREMADE : Publications
Metadata
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Author
Bouchard, Bruno
Type
Article accepté pour publication ou publié
Abstract (EN)
We consider a general optimal switching problem for a controlled diffusion and show that its value coincides with the value of a well-suited stochastic target problem associated to a diffusion with jumps. The proof consists in showing that the Hamilton-Jacobi-Bellman equations of both problems are the same and in proving a comparison principle for this equation. This provides a new family of lower bounds for the optimal switching problem, which can be computed by Monte-Carlo methods. This result has also a nice economical interpretation in terms of a firm's valuation.

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