A GEOMETRIC BROWNIAN MOTION MODEL WITH COMPOUND POISSON PROCESS AND FRACTIONAL STOCHASTIC VOLATILITY

被引：0

作者：

Intarasit, A. ^{[1
]}

Sattayatham, P. ^{[1
]}

机构：

[1] Suranaree Univ Technol, Dept Math, Nakhon Ratchasima, Thailand

来源：

ADVANCES AND APPLICATIONS IN STATISTICS | 2010年 / 16卷 / 01期

关键词：

geometric Brownian motion; compound Poisson process; fractional stochastic volatility; approximate models;

D O I：

暂无

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：

In this paper, we introduce an approximate approach to a geometric Brownian motion (gBm) model with compound Poisson processes and fractional stochastic volatility. Based on a fundamental result on the L-2 -approximation of this fractional noise by semimartingales, we prove a convergence theorem concerning an approximate solution. A simulation example shows a significant reduction of error in a gBm with jump and fractional stochastic volatility as compared to the stochastic volatility.

引用

页码：25 / 47

页数：23

共 43 条

[1] Stochastic interest model driven by compound Poisson process and Brownian motion with applications in life contingencies
Li, Shilong
Zhao, Xia
Yin, Chuancun
Huang, Zhiyue
QUANTITATIVE FINANCE AND ECONOMICS, 2018, 2 (01): : 246 - 260
[2] The busy cycle of the reflected superposition of Brownian motion and a compound Poisson process
Perry, D
Stadje, W
JOURNAL OF APPLIED PROBABILITY, 2001, 38 (01) : 255 - 261
[3] Incorporating stochastic volatility and long memory into geometric Brownian motion model to forecast performance of Standard and Poor's 500 index
Alhagyan, Mohammed
Yassen, Mansour F.
AIMS MATHEMATICS, 2023, 8 (08): : 18581 - 18595
[4] Threshold regression asymptotics: From the compound Poisson process to two-sided Brownian motion
Yu, Ping
Phillips, Peter C. B.
ECONOMICS LETTERS, 2018, 172 : 123 - 126
[5] Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion
Bratian, Vasile
Acu, Ana-Maria
Oprean-Stan, Camelia
Dinga, Emil
Ionescu, Gabriela-Mariana
MATHEMATICS, 2021, 9 (22)
[6] FORECASTING THE PERFORMANCE OF TADAWUL ALL SHARE INDEX (TASI) USING GEOMETRIC BROWNIAN MOTION AND GEOMETRIC FRACTIONAL BROWNIAN MOTION
Alhagyan, Mohammed
Alduais, Fuad
ADVANCES AND APPLICATIONS IN STATISTICS, 2020, 62 (01) : 55 - 65
[7] THE EFFECT OF INCORPORATING MEMORY AND STOCHASTIC VOLATILITY INTO GEOMETRIC BROWNIAN MOTION IN FORECASTING THE PERFORMANCE OF TADAWUL ALL SHARE INDEX (TASI)
Abbas, Anas
Alhagyan, Mohammed
ADVANCES AND APPLICATIONS IN STATISTICS, 2022, 74 : 47 - 62
[8] A New Approach in Geometric Brownian Motion Model
Azizi, Seyed Mohammad Esmaeil Pour Mohammad
Neisy, Abdolsadeh
FUZZY INFORMATION AND ENGINEERING AND DECISION, 2018, 646 : 336 - 342
[9] The generalization of a class of impulse stochastic control models of a geometric Brownian motion
LIU XiaoPeng & LIU KunHui College of Science
Science China(Information Sciences), 2009, (06) : 983 - 998
[10] The generalization of a class of impulse stochastic control models of a geometric Brownian motion
XiaoPeng Liu
KunHui Liu
Science in China Series F: Information Sciences, 2009, 52 : 983 - 998

← 1 2 3 4 5 →