A higher order approximation method for jump-diffusion SDEs with disc...

In this talk we present a strong approximation result for the solution of jump-diffusion stochastic differential equations with discontinuous drift, possibly degenerate diffusion coefficient, and Lipschitz jump-diffusion. We construct a transformation-based jump-adapted quasi-Milstein scheme, which has convergence order 3/4 under additional piecewise smoothness assumptions to the drift and diffusion coefficient. To obtain this result we show that under slightly stronger assumptions on the coefficients the jump-adapted quasi-Milstein scheme also has convergence order 3/4.

This is joint work with Paweł Przybyłowicz and Michaela Szölgyenyi.