  The CEV model is given by the stochastic differential equation
$X_t=X_0+\int_0^t\mu X_sds+\int_0^t\sigma (X^+_s)^pdW_s$, $\frac{1}{2}\le p<1$.
It features a non-Lipschitz diffusion coefficient and gets absorbed at zero
with a positive probability. We show the weak convergence of Euler-Maruyama
approximations $X_t^n$ to the process $X_t$, $0\le t\le T$, in the Skorokhod
metric. We give a new approximation by continuous processes which allows to
relax some technical conditions in the proof of weak convergence in \cite{HZa}
done in terms of discrete time martingale problem. We calculate ruin
probabilities as an example of such approximation. We establish that the ruin
probability evaluated by simulations is not guaranteed to converge to the
theoretical one, because the point zero is a discontinuity point of the
limiting distribution. To establish such convergence we use the Levy metric,
and also confirm the convergence numerically. Although the result is given for
the specific model, our method works in a more general case of non-Lipschitz
diffusion with absorbtion.
