Penalty approach to the HJB equation arising in European stock option pricing with proportional transaction costs

W. Li, Song Wang

    Research output: Contribution to journalArticle

    23 Citations (Scopus)

    Abstract

    We present a novel penalty approach to the Hamilton-Jacobi-Bellman (HJB) equation arising from the valuation of European options with proportional transaction costs. We first approximate the HJB equation by a quasilinear 2nd-order partial differential equation containing two linear penalty terms with penalty parameters λ 1 and λ 2 respectively. Then, we show that there exists a unique viscosity solution to the penalized equation. Finally, we prove that, when both λ 1 and λ 2 approach infinity, the viscosity solution to the penalized equation converges to that of the corresponding original HJB equation.
    Original languageEnglish
    Pages (from-to)279-293
    JournalJournal of Optimization Theory and Applications
    Volume143
    Issue number2
    DOIs
    Publication statusPublished - 2009

    Fingerprint

    Hamilton-Jacobi-Bellman Equation
    Transaction Costs
    Option Pricing
    Penalty
    Directly proportional
    Viscosity Solutions
    Viscosity
    Partial differential equations
    Costs
    European Options
    Valuation
    Partial differential equation
    Infinity
    Converge
    Term
    Proportional transaction costs
    Option pricing
    Stock options
    Hamilton-Jacobi-Bellman equation
    Viscosity solutions

    Cite this

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    abstract = "We present a novel penalty approach to the Hamilton-Jacobi-Bellman (HJB) equation arising from the valuation of European options with proportional transaction costs. We first approximate the HJB equation by a quasilinear 2nd-order partial differential equation containing two linear penalty terms with penalty parameters λ 1 and λ 2 respectively. Then, we show that there exists a unique viscosity solution to the penalized equation. Finally, we prove that, when both λ 1 and λ 2 approach infinity, the viscosity solution to the penalized equation converges to that of the corresponding original HJB equation.",
    author = "W. Li and Song Wang",
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    language = "English",
    volume = "143",
    pages = "279--293",
    journal = "Journal of Optimisation Theory and Applications",
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    Penalty approach to the HJB equation arising in European stock option pricing with proportional transaction costs. / Li, W.; Wang, Song.

    In: Journal of Optimization Theory and Applications, Vol. 143, No. 2, 2009, p. 279-293.

    Research output: Contribution to journalArticle

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    AU - Wang, Song

    PY - 2009

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    AB - We present a novel penalty approach to the Hamilton-Jacobi-Bellman (HJB) equation arising from the valuation of European options with proportional transaction costs. We first approximate the HJB equation by a quasilinear 2nd-order partial differential equation containing two linear penalty terms with penalty parameters λ 1 and λ 2 respectively. Then, we show that there exists a unique viscosity solution to the penalized equation. Finally, we prove that, when both λ 1 and λ 2 approach infinity, the viscosity solution to the penalized equation converges to that of the corresponding original HJB equation.

    U2 - 10.1007/s10957-009-9559-7

    DO - 10.1007/s10957-009-9559-7

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    JO - Journal of Optimisation Theory and Applications

    JF - Journal of Optimisation Theory and Applications

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