Numerical approximation of stochastic differential equations with jum...

Stochastic differential equations (SDEs) with jump noise have applications in various areas of finance, insurance, and economics. In these contexts, however, the regularity assumptions of the standard literature are often not met, such as in control problems where discontinuous coefficients occur. Since explicit solutions are hardly available, numerical approximations are crucial for the utilisation of these models. In this talk we focus on jump-diffusion SDEs with discontinuous drift and present results on their numerical approximation. We introduce the so-called transformation-based jump-adapted quasi-Milstein scheme and provide a complete error analysis: We prove convergence of order 3/4 in L^p for p ≥1. Furthermore, we show lower error bounds for non-adaptive and jump-adapted approximation schemes of order 3/4 in L^1. We conclude the optimality of the transformation-based jump-adapted quasi-Milstein scheme.