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.

LAPLACE TRANSFORMS AND INSTALLMENT OPTIONS

2004 ◽  
Vol 14 (08) ◽  
pp. 1167-1189 ◽  
Author(s):  
GHADA ALOBAIDI ◽  
ROLAND MALLIER ◽  
A. STANLEY DEAKIN
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Integral Equation ◽  
Free Boundary ◽  
Asymptotic Analysis ◽  
Laplace Transform ◽  
Financial Security ◽  
Present Value ◽  
Lump Sum ◽  
A Free Boundary Problem

An installment option is a derivative financial security where the price is paid in installments instead of as a lump sum at the time of purchase. The valuation of these options involves a free boundary problem in that at each installment date, the holder of the derivative has the option of continuing to pay the premiums or allowing the contract to lapse, and the decision will depend upon whether the present value of the expected pay-off is greater or less than the present value of the remaining premiums. Using a model installment option where the premiums are paid continuously rather than on discrete dates, an integral equation is derived for the position of this free boundary by applying a partial Laplace transform to the underlying partial differential equation for the value of the security. Asymptotic analysis of this integral equation allows us to deduce the behavior of the free boundary close to expiry.

Uniqueness of solution to a free boundary problem from combustion with transport

MAT Serie A ◽  
2001 ◽  
Vol 5 ◽  
pp. 37-41
Author(s):  
Claudia Lederman ◽  
Juan Luis Vázquez ◽  
Noemí Wolanski
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Uniqueness Of Solution ◽  
A Free Boundary Problem

EXISTENCE OF PERIODIC SOLUTIONS FOR A FREE BOUNDARY PROBLEM OF HYPERBOLIC TYPE

2008 ◽  
Vol 05 (04) ◽  
pp. 785-806
Author(s):  
KAZUAKI NAKANE ◽  
TOMOKO SHINOHARA
Keyword(s):  
Mathematical Model ◽  
Free Boundary ◽  
Hyperbolic Equation ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Physical Phenomenon ◽  
Hyperbolic Type ◽  
Existence Of Periodic Solutions ◽  
A Free Boundary Problem ◽  
Thin Tape

A free boundary problem that arises from the physical phenomenon of "peeling a thin tape from a domain" is treated. In this phenomenon, the movement of the tape is governed by a hyperbolic equation and is affected by the peeling front. We are interested in the behavior of the peeling front, especially, the phenomenon of self-excitation vibration. In the present paper, a mathematical model of this phenomenon is proposed. The cause of this vibration is discussed in terms of adhesion.

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