Higher-order approximation and optimality of jump-diffusion SDEs with...

In this talk we consider the approximation of jump-diffusion stochastic differential equations with discontinuous drift, possibly degenerate diffusion coefficient, and Lipschitz continuous jump coefficient. We present a jump-adapted higher-order scheme, the so-called transformation-based jump-adapted quasi-Milstein scheme. For this scheme, we provide a complete error analysis: We prove convergence order 3/4 in L^p for p∈[1,∞). Further, we provide lower error bounds for non-adaptive and jump-adapted approximation schemes of order 3/4 in L¹. This yields optimality of the transformation-based jump-adapted quasi-Milstein scheme.

This is joint work with Paweł Przybyłowicz and Michaela Szölgyenyi.