TY - JOUR
T1 - Penalty approach to the HJB equation arising in European stock option pricing with proportional transaction costs
AU - Li, W.
AU - Wang, Song
PY - 2009
Y1 - 2009
N2 - 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.
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
M3 - Article
VL - 143
SP - 279
EP - 293
JO - Journal of Optimisation Theory and Applications
JF - Journal of Optimisation Theory and Applications
SN - 0022-3239
IS - 2
ER -