%0 Journal Article %T Option pricing with transaction costs and a nonlinear Black--Scholes equation %A G. Barles %A H. M. Soner %J Finance Stoch. %D 1998 %V 2 %F Barles1998 %0 Journal Article %T The pricing of options and corporate liabilities %A F. Black %A M. Scholes %J J. Polit. Econ. %D 1973 %V 81 %F Black1973 %0 Journal Article %T Numerical analysis and simulation of option pricing problems modeling illiquid markets %A R. Company %A L. Jódar %A E. Ponsoda %A C. Ballester %J Comput. Math. Appl. %D 2010 %V 59 %F Company2010 %0 Journal Article %T A high-order compact method for nonlinear Black--Scholes option pricing equations of American options %A E. Dremkova %A M. Ehrhardt %J Int. J. Comput. Math. %D 2011 %V 88 %F Dremkova2011 %0 Journal Article %T Discrete maximum principle and adequate discretizations of linear parabolic problems %A I. Faragó %A R. Horváth %J SIAM J. Sci. Comput. %D 2006 %V 28 %F Faragó2006 %0 Book %T Partial Differential Equations of Parabolic Type %A A. Friedman %D 1964 %I Prentice-Hall %C Englewood Cliffs %F Friedman1964 %0 Book %T Difference Schemes (in Russian) %A S. K. Godunov %A V. S. Ryaben'kii %D 1977 %I Nauka %C Moscow %F Godunov1977 %0 Journal Article %T General properties of solutions to inhomogeneous Black--Scholes equations with discontinuous maturity payoffs %A O. Hyong-Chol %A J. J. Jo %A J. S. Kim %J J. Differential Equations %D 2016 %V 260 %F Hyong-Chol2016 %0 Journal Article %T Second order monotone difference schemes with approximation on non-uniform grids for two-dimensional quasilinear parabolic convection-diffusion equations %A L. M. Hieu %A D. N. H. Thanh %A S. Prasath %J Vestnik St. Petersburg University, Mathematics %D 2020 %V 53 %F Hieu2020 %0 Journal Article %T On the risk-adjusted pricing-methodology-based valuation of vanilla options and explanation of the volatility smile %A M. Jandačka %A D. Ševčovič %J J. Appl. Math. %D 2005 %V 3 %F Jandačka2005 %0 Journal Article %T A second-order positivity preserving numerical method for Gamma equation %A M. N. Koleva %A L. G. Vulkov %J Appl. Math. Comput. %D 2013 %V 220 %F Koleva2013 %0 Book %T Linear and Quasilinear Equations of Parabolic Type (in Russian) %A O. A. Ladyženskaja %A V. A. Solonnikov %A N. N. Ural'ceva %D 1967 %I Nauka %C Moscow %F Ladyženskaja1967 %0 Journal Article %T Maximum principle for finite-difference schemes with non sign-constant input data (in Russian) %A P. Matus %A L. M. Hieu %A L. G. Vulkov %J Dokl. Nats. Akad. Nauk Belarusi %D 2015 %V 59 %F Matus2015 %0 Journal Article %T Monotone finite-difference schemes of second-order accuracy for quasilinear parabolic equations with mixed derivatives %A P. Matus %A L. M. Hieu %A D. Pylak %J Diff. Equ. %D 2019 %V 55 %F Matus2019 %0 Journal Article %T Analysis of second order difference schemes on non-uniform grids for quasilinear parabolic equations %A P. Matus %A L. M. Hieu %A L. G. Vulkov %J J. Comput. Appl. Math. %D 2017 %V 310 %F Matus2017 %0 Journal Article %T On convergence of difference schemes for dirichlet IBVP for two-dimensional quasilinear parabolic equations with mixed derivatives and generalized solutions %A P. Matus %A D. Poliakov %A L. M. Hieu %J Comput. Meth. Appl. Math. %D 2020 %V %F Matus2020 %0 Journal Article %T Monotone difference schemes for linear parabolic equations with mixed boundary conditions (in Russian) %A P. P. Matus %A V. T. K. Tuyen %A F. Z. Gaspar %J Dokl. Nats. Akad. Nauk Belarusi %D 2014 %V 58 %F Matus2014 %0 Book %T The Theory of Difference Schemes %A A. Samarskii %D 2001 %I Marcel Dekker %C New York %F Samarskii2001