Convergence of Numerical Approximation for Jump Models Involving Delay and Mean-Reverting Square Root Process

The mean-reverting square root process with jump has been widely used as a model on the financial market. Since the diffusion coefficient in the model does not satisfy the linear growth condition and local Lipschitz condition, we can not examine its properties by traditional techniques. To overcome...

Full description

Saved in:
Bibliographic Details
Published in:Stochastic analysis and applications 2011-03, Vol.29 (2), p.216-236
Main Authors: Jiang, Feng, Shen, Yi, Wu, Fuke
Format: Article
Language:English
Subjects:
Applications
Approximation
Bonding
Compensated Poisson process
Convergence
Delay
Euler-Maruyama method
Exact sciences and technology
Insurance, economics, finance
Lipschitz condition
Markov processes
Mathematical analysis
Mathematical models
Mathematics
Mean-reverting square root process
Probability and statistics
Probability theory and stochastic processes
Roots
Sciences and techniques of general use
Statistics
Stochastic analysis
Stochastic processes
Strong convergence
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The mean-reverting square root process with jump has been widely used as a model on the financial market. Since the diffusion coefficient in the model does not satisfy the linear growth condition and local Lipschitz condition, we can not examine its properties by traditional techniques. To overcome the difficulties, we develop several new techniques to examine the numerical method of jump models involving delay and mean-reverting square root. We show that the numerical approximate solutions converge to the true solutions. Finally, we apply the convergence to examine a path-dependent option price and a bond in the financial pricing.
ISSN:0736-2994
1532-9356
DOI:10.1080/07362994.2011.532043