Penalty Approach to the HJB Equation Arising in European Stock Option Pricing with Proportional Transaction Costs |
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Authors: | W. Li S. Wang |
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Affiliation: | (2) Department of Mathematics, Saitama University, Saitama, Japan; |
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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. |
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