## Abstract

The CEV model is given by the stochastic differential equation X _{t} = X_{o} + ∫_{o}, μX_{s}ds+ ∫_{o} ∼(X^{+}_{s})^{p}dW_{s}, 1/2 ≤ 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 ≤ t ≤ T, in the Skorokhod metric, by giving a new approximation by continuous processes. We calculate ruin probabilities as an example of such approximation. The ruin probability evaluated by simulations is not guaranteed to converge to the theoretical one, because the limiting distribution is discontinuous at zero. To approximate the size of the jump at zero we use the Levy metric, and also confirm the convergence numerically.

Original language | English |
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Pages (from-to) | 1-14 |

Number of pages | 14 |

Journal | Discrete and Continuous Dynamical Systems - Series B |

Volume | 16 |

Issue number | 1 |

DOIs | |

State | Published - Jul 2011 |

## Keywords

- Absorbtion
- CEV model
- Euler-Maruyama algorithm
- Non-Lipschitz diffusion
- Weak convergence