The Euler-Maruyama approximations for the CEV model

Vyacheslav M. Abramov, Fima C. Klebaner, Robert Sh Liptser

Research output: Contribution to journalArticlepeer-review


The CEV model is given by the stochastic differential equation X t = Xo + ∫o, μXsds+ ∫o ∼(X+s)pdWs, 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 Xtn 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 languageEnglish
Pages (from-to)1-14
Number of pages14
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number1
StatePublished - Jul 2011


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


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