Penalty Approach to the HJB Equation Arising in European Stock Option Pricing with Proportional Transaction Costs

W. Li and S. Wang ()
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W. Li: University of Western Australia
S. Wang: University of Western Australia

Journal of Optimization Theory and Applications, 2009, vol. 143, issue 2, No 4, 279-293

Abstract: 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.

Keywords: Penalty approach; European option pricing; Optimal control; Partial differential equation; Viscosity solution (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (10)

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DOI: 10.1007/s10957-009-9559-7

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