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Proportional Transaction Costs in the Robust Control Approach to Option Pricing: The Uniqueness Theorem

Author

Listed:
  • Naïma El Farouq

    (LIMOS - Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes - UBP - Université Blaise Pascal - Clermont-Ferrand 2 - UdA - Université d'Auvergne - Clermont-Ferrand I - SIGMA Clermont - SIGMA Clermont - ENSM ST-ETIENNE - Ecole Nationale Supérieure des Mines de St Etienne - CNRS - Centre National de la Recherche Scientifique)

  • Pierre Bernhard

    (BIOCORE - Biological control of artificial ecosystems - LOV - Laboratoire d'océanographie de Villefranche - OOVM - Observatoire océanologique de Villefranche-sur-mer - UPMC - Université Pierre et Marie Curie - Paris 6 - INSU - CNRS - Institut national des sciences de l'Univers - CNRS - Centre National de la Recherche Scientifique - UPMC - Université Pierre et Marie Curie - Paris 6 - INSU - CNRS - Institut national des sciences de l'Univers - CNRS - Centre National de la Recherche Scientifique - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique - INRA - Institut National de la Recherche Agronomique)

Abstract

We prove the missing uniqueness theorem for the viscosity solution of a quasi-variational inequality related to a minimax impulse control problem modeling the option pricing with proportional transactions costs. This result makes our robust control approach of option pricing in the interval market model essentially complete.

Suggested Citation

  • Naïma El Farouq & Pierre Bernhard, 2015. "Proportional Transaction Costs in the Robust Control Approach to Option Pricing: The Uniqueness Theorem," Post-Print hal-01090616, HAL.
    • Handle: RePEc:hal:journl:hal-01090616
    DOI: 10.1007/s00245-014-9276-y
    Note: View the original document on HAL open archive server: https://inria.hal.science/hal-01090616
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    References listed on IDEAS

    as
    1. Pierre Bernhard, 2006. "On The Singularities Of An Impulsive Differential Game Arising In Mathematical Finance," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 219-229.
    2. Pierre Bernhard, 2005. "The Robust Control Approach to Option Pricing and Interval Models: An Overview," Springer Books, in: Michèle Breton & Hatem Ben-Ameur (ed.), Numerical Methods in Finance, chapter 0, pages 91-108, Springer.
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    Keywords

    viscosity solutions; robust control; Option pricing;
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