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The Finite Horizon Optimal Multi-Modes Switching Problem: The Viscosity Solution Approach

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Abstract

In this paper we show existence and uniqueness of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. This system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem. The switching cost functions are arbitrary. This problem is in relation with the valuation of firms in a financial market.

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Authors and Affiliations

  1. Dépt. de Mathématiques, Equipe Stat. et Processus, Université du Maine, Avenue Olivier Messiaen, 72085, Le Mans, Cedex 9, France

    Brahim El Asri & Said Hamadene

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  1. Brahim El Asri
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  2. Said Hamadene
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Correspondence to Said Hamadene.

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Communicated by Bernt Oksendal.

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El Asri, B., Hamadene, S. The Finite Horizon Optimal Multi-Modes Switching Problem: The Viscosity Solution Approach. Appl Math Optim 60, 213–235 (2009). https://doi.org/10.1007/s00245-009-9071-3

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  • DOI: https://doi.org/10.1007/s00245-009-9071-3

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