Abstracts

We consider the approximation of stochastic differential equations (SDEs) with non-Lipschitz drift or diffusion coefficients. We present a modified explicit Euler-Maruyama discretisation scheme that allows us to prove strong convergence, with a rate. Under some regularity conditions, we obtain the \textit{optimal} strong error rate of $1/2$. We consider SDEs popular in the mathematical finance literature, including the Cox-Ingersoll-Ross, the $3/2$ and the Ait-Sahalia models, as well as a family of mean-reverting processes with locally smooth coefficients.