Sankhya: The Indian Journal of Statistics

1996, Volume 58, Series A, Pt. 1, pp. 25--47

MEAN-SQUARE EFFICIENT NUMERICAL SOLUTION OF JUMP-DIFFUSION STOCHASTIC DIFFERENTIAL EQUATIONS

By

Y. MAGHSOODI, University of Southampton

SUMMARY.  In this paper the Taylor expansions in the semi-group of conditional expectations are truncated to derive new efficient schemes for the numerical solution of jump-diffusion stochastic differential equations. These schemes are proven to converge in mean square with the best possible order rate which is the second order in the grid size. A generalized integration by parts formula is applied to derive exact digitally computable evaluations of the multiple stochastic integrals which arise in the schemes. Simulation results are consistent with the theoretical findings.

AMS (1991) subject classification.  Primary 60H10, 60J35; secondary 62L20, 93E30,  .

Key words and phrases. Stochastic differential equation, Jump-diffusions, Taylor expansions in semi-groups, Discretization.

Full paper (PDF)

This article in Mathematical Reviews.