A Compensated Numerical Method for Solving Stochastic Differential Equations with Variable Delays and Random Jump Magnitudes

Ying Du and Changlin Mei

Mathematical Problems in Engineering, 2015, vol. 2015, 1-11

Abstract:

Stochastic differential equations with jumps are of a wide application area especially in mathematical finance. In general, it is hard to obtain their analytical solutions and the construction of some numerical solutions with good performance is therefore an important task in practice. In this study, a compensated split-step method is proposed to numerically solve the stochastic differential equations with variable delays and random jump magnitudes. It is proved that the numerical solutions converge to the analytical solutions in mean-square with the approximate rate of 1/2. Furthermore, the mean-square stability of the exact solutions and the numerical solutions are investigated via a linear test equation and the results show that the proposed numerical method shares both the mean-square stability and the so-called A-stability.

Date: 2015
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/MPE/2015/810160.pdf (application/pdf)
http://downloads.hindawi.com/journals/MPE/2015/810160.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:810160

DOI: 10.1155/2015/810160

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().