On the First-Passage Area of a One-Dimensional Jump-Diffusion Process

被引：12
|
作者：
Abundo, Mario [1 ]
机构：
[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy
来源：
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2013年 / 15卷 / 01期
关键词：
First-passage time; First-passage area; One-dimensional jump-diffusion; BROWNIAN-MOTION;
D O I：
10.1007/s11009-011-9223-1
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
For a one-dimensional jump-diffusion process X(t), starting from x > 0, it is studied the probability distribution of the area A(x) swept out by X(t) till its first-passage time below zero. In particular, it is shown that the Laplace transform and the moments of A(x) are solutions to certain partial differential-difference equations with outer conditions. The distribution of the maximum displacement of X(t) is also studied. Finally, some explicit examples are reported, regarding diffusions with and without jumps.
引用
收藏
页码：85 / 103
页数：19
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