数学物理学报(英文版) ›› 2000, Vol. 20 ›› Issue (3): 341-358.

• 论文 • 上一篇    下一篇

MULTI-DIMENSIONAL GEOMETRIC BROWNIAN MOTIONS, ONSAGER-MACHLUP FUNCTIONS, AND APPLICATIONS TO MATHEMATICAL FINANCE

 胡耀忠   

  1. Department of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, KS 66045-2142. USA
    Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
  • 收稿日期:1999-04-08 出版日期:2000-05-20 发布日期:2000-05-20
  • 基金资助:

    Partly supported by the General Research Fund of the University of Kansas.
    e-mail:hu math.ukans.edu

MULTI-DIMENSIONAL GEOMETRIC BROWNIAN MOTIONS, ONSAGER-MACHLUP FUNCTIONS, AND APPLICATIONS TO MATHEMATICAL FINANCE

 胡耀忠   

  1. Department of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, KS 66045-2142. USA
    Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
  • Received:1999-04-08 Online:2000-05-20 Published:2000-05-20
  • Supported by:

    Partly supported by the General Research Fund of the University of Kansas.
    e-mail:hu math.ukans.edu

摘要:

The solutions of the following bilinear stochastic differential equation are stud-
ied
dxt =
Xm
k=1
Ak
t xtdwk(t) + Btxtdt
where Ak
t , Bt are (deterministic) continuous matrix-valued functions of t and w1(t), · · ·,
wm(t) are m independent standard Brownian motions. Conditions are given such that the
solution is positive if the initial condition is positive. The equation the most probable path
must satisfy is also derived and applied to a mathematical finance problem.

关键词: Multi-dimensional geometric Brownian motions, Onsager-Machlup func-
tions,
most probable path, positivity, most likely interest rate

Abstract:

The solutions of the following bilinear stochastic differential equation are stud-
ied
dxt =
Xm
k=1
Ak
t xtdwk(t) + Btxtdt
where Ak
t , Bt are (deterministic) continuous matrix-valued functions of t and w1(t), · · ·,
wm(t) are m independent standard Brownian motions. Conditions are given such that the
solution is positive if the initial condition is positive. The equation the most probable path
must satisfy is also derived and applied to a mathematical finance problem.

Key words: Multi-dimensional geometric Brownian motions, Onsager-Machlup func-
tions,
most probable path, positivity, most likely interest rate

中图分类号: 

  • 60H10