Convergence of $\theta$ Euler-Maruyama method for SDEs in Mathematical finance

‎In this paper we are interested in approximation of stochastic differential equations which have non-lipschitz coefficients‎. ‎Motivation comes from finance and biology where many widely applied models‎ ‎do not satisfy the standard assumptions required for the strong convergence‎. ‎We apply $\theta$-Euler-Maruyama method and we show that this method is convergence and also it preserve the domain of the SDE‎. ‎Moreover‎, ‎we conclude this result can be applied to many SDEs we encounter‎ ‎in mathematical finance and bio-mathematics such as CEV and CIR models‎.