EXISTENCE AND UNIQUENESS OF THE SOLUTION OF A FREE BOUNDARY PROBLEM FOR A PARABOLIC COMPLEX EQUATION

2009 ◽  
Author(s):  
YONGZHI XU
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Existence And Uniqueness ◽  
Complex Equation ◽  
Uniqueness Of The Solution ◽  
A Free Boundary Problem

A free boundary problem coming from the perpetual American call options with utility

2012 ◽  
Vol 24 (2) ◽  
pp. 231-271 ◽  
Author(s):  
SONG LIPING ◽  
YU WANGHUI
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Financial Market ◽  
Free Boundary Problem ◽  
Utility Functions ◽  
Call Options ◽  
Line Method ◽  
Uniqueness Of The Solution ◽  
A Free Boundary Problem

A free boundary problem, which comes from the model of the perpetual American call options with utility functions in financial market, is investigated. It is a degenerative parabolic free boundary problem and is studied by the line method. The existence, regularity and uniqueness of the solution as well as some properties of the free boundary are established.

scholarly journals A non-local free boundary problem arising in a theory of financial bubbles

2014 ◽  
Vol 372 (2028) ◽  
pp. 20130404 ◽  
Author(s):  
Henri Berestycki ◽  
Regis Monneau ◽  
José A. Scheinkman
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Existence And Uniqueness ◽  
Obstacle Problem ◽  
Speculative Bubbles ◽  
Financial Bubbles ◽  
Uniqueness Of The Solution ◽  
Non Local ◽  
The Cost

We consider an evolution non-local free boundary problem that arises in the modelling of speculative bubbles. The solution of the model is the speculative component in the price of an asset. In the framework of viscosity solutions, we show the existence and uniqueness of the solution. We also show that the solution is convex in space, and establish several monotonicity properties of the solution and of the free boundary with respect to parameters of the problem. To study the free boundary, we use, in particular, the fact that the odd part of the solution solves a more standard obstacle problem. We show that the free boundary is and describe the asymptotics of the free boundary as c , the cost of transacting the asset, goes to zero.

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
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