Abstract
We present the first higher-order approximation scheme for solutions of jump-diffusion stochastic differential equations with discontinuous drift. For this transformation-based jump-adapted quasi-Milstein scheme, we prove Lp-convergence order 3/4. To obtain this result, we prove that under slightly stronger assumptions (but still weaker than assumptions applied before) a related jump-adapted quasi-Milstein scheme has convergence order 3/4; in a special case it even has convergence order 1. Order 3/4 is conjectured to be optimal.
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