opt1.pdf (116.9 kB)
An Optimization Approach to Weak Approximation of Stochastic Differential Equations with Jumps
journal contribution
posted on 2011-02-08, 10:53 authored by Kenji Kashima, Reiichiro KawaiWe propose an optimization approach to weak approximation of stochastic differential equations with jumps. A mathematical programming technique is employed to obtain numerically upper and lower bound estimates of the expectation of interest, where the optimization procedure ends up with a polynomial programming. A major advantage of our approach is that we do not need to simulate sample paths of jump processes, for which few practical simulation techniques exist. We provide numerical results of moment estimations for Doléans–Dade stochastic exponential, truncated stable Lévy processes and Ornstein–Uhlenbeck-type processes to illustrate that our method is able to capture very well the distributional characteristics of stochastic differential equations with jumps.
History
Citation
Applied Numerical Mathematics, 2011, 61 (5), pp. 641-650Published in
Applied Numerical MathematicsPublisher
Elsevierissn
0168-9274Copyright date
2011Available date
2011-02-08Publisher DOI
Publisher version
http://www.sciencedirect.com/science/article/pii/S0168927411000110Language
enAdministrator link
Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC