Geodesic
Computational technique for treating the nonlinear Black-Scholes equation with the effect of transaction costs
Kybernetika, Tome 43 (2007) no. 6, pp. 807-815.

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We deal with numerical computation of the nonlinear partial differential equations (PDEs) of Black–Scholes type which incorporate the effect of transaction costs. Our proposed technique surmounts the difficulty of infinite domains and unbounded values of the solutions. Numerical implementation shows the validity of our scheme.
Classification : 35K15, 65M99, 91B28
Keywords: transaction costs; nonlinear partial differential equation; numerical computation 
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     author = {Imai, Hitoshi and Ishimura, Naoyuki and Sakaguchi, Hideo},
     title = {Computational technique for treating the nonlinear {Black-Scholes} equation with the effect of transaction costs},
     journal = {Kybernetika},
     pages = {807--815},
     publisher = {mathdoc},
     volume = {43},
     number = {6},
     year = {2007},
     mrnumber = {2388395},
     zbl = {1213.91160},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007__43_6_a5/}
}
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Imai, Hitoshi; Ishimura, Naoyuki; Sakaguchi, Hideo. Computational technique for treating the nonlinear Black-Scholes equation with the effect of transaction costs. Kybernetika, Tome 43 (2007) no. 6, pp. 807-815. http://geodesic.mathdoc.fr/item/KYB_2007__43_6_a5/