کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
7154688 1462583 2018 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Symmetry reduction and exact solutions of the non-linear Black-Scholes equation
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
پیش نمایش صفحه اول مقاله
Symmetry reduction and exact solutions of the non-linear Black-Scholes equation
چکیده انگلیسی
In this paper, we investigate the non-linear Black-Scholes equation: ut+ax2uxx+bx3uxx2+c(xux−u)=0,a,b>0,c≥0.and show that the one can be reduced to the equation ut+(uxx+ux)2=0by an appropriate point transformation of variables. For the resulting equation, we study the group-theoretic properties, namely, we find the maximal algebra of invariance of its in Lie sense, carry out the symmetry reduction and seek for a number of exact group-invariant solutions of the equation. Using the results obtained, we get a number of exact solutions of the Black-Scholes equation under study and apply the ones to resolving several boundary value problems with appropriate from the economic point of view terminal and boundary conditions.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 62, September 2018, Pages 164-173
نویسندگان
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