scholarly journals A free boundary problem for a nonlinear second order differential equation involving a small parameter

1992 ◽  
Vol 44 (2) ◽  
pp. 233-242 ◽  
Author(s):  
Jun Yu Wang ◽  
Da Wei Zheng ◽  
Xue Kong Wang
Keyword(s):  
Differential Equation ◽  
Free Boundary ◽  
Small Parameter ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Order Differential Equation ◽  
Second Order ◽  
Second Order Differential Equation ◽  
A Free Boundary Problem

scholarly journals Laplace Transform Methods for a Free Boundary Problem of Time-Fractional Partial Differential Equation System

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Zhiqiang Zhou ◽  
Xuemei Gao
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Free Boundary ◽  
Laplace Transform ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Fractional Partial Differential Equation ◽  
Partial Differential ◽  
Problem Of Time ◽  
A Free Boundary Problem

We study the pricing of the American options with fractal transmission system under two-state regime switching models. This pricing problem can be formulated as a free boundary problem of time-fractional partial differential equation (FPDE) system. Firstly, applying Laplace transform to the governing FPDEs with respect to the time variable results in second-order ordinary differential equations (ODEs) with two free boundaries. Then, the solutions of ODEs are expressed in an explicit form. Consequently the early exercise boundaries and the values for the American option are recovered using the Gaver-Stehfest formula. Numerical comparisons of the methods with the finite difference methods are carried out to verify the efficiency of the methods.

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