Numerical Treatment to a Non-local Parabolic Free Boundary Problem Arising in Financial Bubbles

被引：0
|
作者：
Arakelyan, Avetik [1 ]
Barkhudaryan, Rafayel [2 ]
Shahgholian, Henrik [3 ]
Salehi, Mohammad [4 ]
机构：
[1] NAS Armenia, Inst Math, Yerevan 0019, Armenia
[2] Amer Univ Armenia, Inst Math, NAS Armenia, Yerevan 0019, Armenia
[3] Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden
[4] Qatar Univ, Dept Math Stat & Phys, POB 2713, Doha, Qatar
来源：
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY | 2019年 / 45卷 / 01期
关键词：
Finite difference method; Viscosity solution; Free boundaries; Obstacle problem; Black-Scholes equation; FINITE-DIFFERENCE SCHEME; OBSTACLE PROBLEM; ERROR ESTIMATE;
D O I：
10.1007/s41980-018-0119-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we continue to study a non-local free boundary problem arising in financial bubbles. We focus on the parabolic counterpart of the bubble problem and suggest an iterative algorithm which consists of a sequence of parabolic obstacle problems at each step to be solved, that in turn gives the next obstacle function in the iteration. The convergence of the proposed algorithm is proved. Moreover, we consider the finite difference scheme for this algorithm and obtain its convergence. At the end of the paper, we present and discuss computational results.
引用
收藏
页码：59 / 73
页数：15
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