An adaptive extrapolation discontinuous Galerkin method for the valuation of Asian options

被引：6

作者：

Marcozzi, Michael D. ^{[1
]}

机构：

[1] Univ Nevada, Dept Math Sci, Las Vegas, NV 89154 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2011年 / 235卷 / 12期

基金：

美国国家科学基金会;

关键词：

Optimal stopping; Ultraparabolic equations; Discontinuous Galerkin method; Extrapolation; Asian options; CONSERVATION-LAWS; ULTRAPARABOLIC EQUATION; DIFFERENTIAL-EQUATIONS; VISCOSITY SOLUTIONS; ERROR ESTIMATION; BROWNIAN-MOTION; ULTRADIFFUSION;

D O I：

10.1016/j.cam.2011.02.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the approximation of the optimal stopping problem associated with ultradiffusion processes in the context of mathematical finance and the valuation of Asian options. In particular, the value function is characterized as the solution of an ultraparabolic variational inequality. Employing the penalty method and a regularization of the state space, we develop higher-order adaptive approximation schemes which utilize the extrapolation discontinuous Galerkin method in temporal space. Numerical examples are provided in order to demonstrate the approach. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：3632 / 3645

页数：14

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