An explicit Euler scheme with strong rate of convergence for non-Lipschitz SDEs

We consider the approximation of stochastic dierential equations (SDEs) with non-Lipschitz drift or diusion coecients. We present a modified explicit EulerMaruyama discretisation scheme that allows us to prove strong convergence, with a rate. Under some regularity conditions, we obtain the optimal strong error rate. We consider SDEs popular in the mathematical finance literature, including the Cox-Ingersoll-Ross (CIR), the 3=2 and the Ait-Sahalia models, as well as a family of mean-reverting processes with locally smooth coecients.

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