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

    27 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

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