尤拉方程在半无界区域的边值问题的基本解

Basic Solution on the Boundary Value Problem of Euler Equation on Semi Infinite Domain

摘要: 本文把永久美式期权确定最佳实施边界的问题归结为尤拉方程在半无界区域的边值问题的基本解来研究。获得了基本解的表达式，同时确定了基本解的奇异点。证明了基本解在半无界区域连续，但解的导数在奇异点发生间断，在奇异点处基本解取最大值。基本解的奇异点就是永久美式期权最佳实施边界点。

Abstract: In this paper, the permanent American options determine optimal exercise boundary problem is boiling down to the Euler equation in a semi infinite domain boundary value problem of the basic solution to study. We obtained the expression of the basic solution and the singular point of the basic solution. It is proved that the basic solution is continuous in the semi infinite domain, but the derivative of the solution is discontinuous at the singular point. The maximum value is obtained in the singular point. The singular point of the basic solution is the best implementation point of the permanent American option.