SEMI-LAGRANGIAN SCHEMES FOR LINEAR AND FULLY NON-LINEAR HAMILTON-JACOBI-BELLMAN EQUATIONS

被引：0
|
作者：
Debrabant, Kristian [1 ]
Jakobsen, Espen Robstad [2 ]
机构：
[1] Univ Southern Denmark, Dept Math & Comp Sci, Campusvej 55, DK-5230 Odense M, Denmark
[2] Norwegian Univ Sci & Technol, NO-7491 Trondheim, Norway
来源：
HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS | 2014年 / 8卷
关键词：
Monotone approximation schemes; difference-interpolation methods; stability; convergence; error bound; degenerate parabolic equations; Hamilton-Jacobi-Bellman equations; viscosity solution; APPROXIMATION;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the numerical solution of Hamilton-Jacobi-Bellman equations arising in stochastic control theory. We introduce a class of monotone approximation schemes relying on monotone interpolation. These schemes converge under very weak assumptions, including the case of arbitrary degenerate diffusions. Besides providing a unifying framework that includes several known first order accurate schemes, stability and convergence results are given, along with two different robust error estimates. Finally, the method is applied to a super-replication problem from finance.
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页码：483 / 490
页数：8
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