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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Institution: | (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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Keywords: | |
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