Higher-order approximation of jump-diffusion McKean--Vlasov SDEs

In this talk we study the numerical approximation of the jump-diffusion McKean--Vlasov SDEs with super-linearly growing drift, diffusion and jump-coefficient. In the first step, we derive the corresponding interacting particle system and define a Milstein-type approximation for this. Making use of the propagation of chaos result and investigating the error of the Milstein-type scheme we provide convergence results for the scheme. In a second step, we discuss potential simplifications of the numerical approximation scheme for the direct approximation of the jump-diffusion McKean--Vlasov SDE. Lastly, we present the results of our numerical simulations.