Computational technique for treating the nonlinear Black-Scholes equation with the effect of transaction costs

Hitoshi Imai; Naoyuki Ishimura; Hideo Sakaguchi

Kybernetika (2007)

  • Volume: 43, Issue: 6, page 807-815
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Imai, Hitoshi, Ishimura, Naoyuki, and Sakaguchi, Hideo. "Computational technique for treating the nonlinear Black-Scholes equation with the effect of transaction costs." Kybernetika 43.6 (2007): 807-815. <http://eudml.org/doc/33898>.

@article{Imai2007,
abstract = {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.},
author = {Imai, Hitoshi, Ishimura, Naoyuki, Sakaguchi, Hideo},
journal = {Kybernetika},
keywords = {transaction costs; nonlinear partial differential equation; numerical computation},
language = {eng},
number = {6},
pages = {807-815},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Computational technique for treating the nonlinear Black-Scholes equation with the effect of transaction costs},
url = {http://eudml.org/doc/33898},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Imai, Hitoshi
AU - Ishimura, Naoyuki
AU - Sakaguchi, Hideo
TI - Computational technique for treating the nonlinear Black-Scholes equation with the effect of transaction costs
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 6
SP - 807
EP - 815
AB - 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.
LA - eng
KW - transaction costs; nonlinear partial differential equation; numerical computation
UR - http://eudml.org/doc/33898
ER -

References

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  7. Imai H., Ishimura N., Mottate, I., Nakamura M. A., 10.1007/s10690-007-9047-8, Asia–Pacific Financial Markets 13 (2007), 315–326 DOI10.1007/s10690-007-9047-8
  8. Ishimura N., Remarks on the nonlinear partial differential equations of Black–Scholes type with transaction costs, preprint. Submitted 
  9. Jandačka M., Ševčovič D., 10.1155/JAM.2005.235, J. Appl. Math. 3 (2005), 235–258 Zbl1128.91025MR2201973DOI10.1155/JAM.2005.235
  10. Kwok Y., Mathematical Models of Financial Derivatives, Springer, New York 1998 Zbl1146.91002MR1645143
  11. Leland H. E., 10.1111/j.1540-6261.1985.tb02383.x, J. Finance 40 (1985), 1283–1301 (1985) DOI10.1111/j.1540-6261.1985.tb02383.x
  12. Merton R. C., 10.2307/3003143, Bell J. Econ. Manag. Sci. 4 (1973), 141–183 (1973) MR0496534DOI10.2307/3003143
  13. Wilmott P., Paul Wilmott on Quantitative Finance, Vol, I, II. Wiley, New York 2000 
  14. Wilmott P., Howison, S., Dewynne J., The Mathematics of Financial Derivatives, Cambridge University Press, Cambridge 1995 Zbl0842.90008MR1357666

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