Multidimensional investment problem

被引：8

作者：

Christensen, Soeren ^{[1
]}

Salminen, Paavo ^{[2
]}

机构：

[1] Univ Hamburg, Dept Math, Res Grp Stat & Stochast Proc, Bundesstr 55 Geomatikum, D-20146 Hamburg, Germany

[2] Abo Akad Univ, Fac Sci & Engn, SF-20500 Turku, Finland

来源：

MATHEMATICS AND FINANCIAL ECONOMICS | 2018年 / 12卷 / 01期

关键词：

Geometric Brownian motion; Convex set; Resolvent kernel; Duality; Integral representation of excessive function; Optimal investment problem; American put option; Integral equation; OPTIMAL STOPPING GAMES; AMERICAN; STOCK;

D O I：

10.1007/s11579-017-0195-y

中图分类号：

F8 [财政、金融];

学科分类号：

0202 ;

摘要：

In this paper we demonstrate that the Riesz representation of excessive functions is a useful and enlightening tool to study optimal stopping problems. After a short general discussion of the Riesz representation we concretize to geometric Brownian motions. After this, a classical investment problem, also known as exchange-of-baskets-problem, is studied. It is seen that the boundary of the stopping region in this problem can be characterized as a unique solution of an integral equation arising immediately from the Riesz representation of the value function. The two-dimensional case is studied in more detail and a numerical algorithm is presented.

引用

页码：75 / 95

页数：21

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