Work

On explicit approximations for Lévy driven SDEs with super-linear diffusion coefficients

Year: 2017

Type: article

Abstract: Motivated by the results of [21], we propose explicit Euler-type schemes for SDEs with random coefficients driven by Lévy noise when the drift and diffusion coefficients can grow super-linearly. As an application of our results, one can construct explicit Euler-type schemes for SDEs with delays (SDDEs) which are driven by Lévy noise and have super-linear coefficients. Strong convergence results are established and their rate of convergence is shown to be equal to that of the classical Euler scheme. It is proved that the optimal rate of convergence is achieved for $\mathcal{L} ^2$-convergence which is consistent with the corresponding results available in the literature.

Source: Electronic Journal of Probability

DOI: 10.1214/17-ejp89

Authors: Chaman Kumar, Sotirios Sabanis

Institutions: Indian Institute of Technology Roorkee, University of Edinburgh

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $675

OpenAlex ID: W2566160765