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- The Euler-Maruyama approximations for the CEV model
- Abramov, Vyacheslav M.; Klebaner, Fima C.; Liptser, Robert Sh.
- The CEV model is given by the stochastic differential equation X t = X o + ∫ o, μX sds+ ∫ o ∼(X + s) pdW 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.
- Publication type
- Journal article
- Discrete and Continuous Dynamical Systems: Series B, Vol. 16, no. 1 (Jul 2011), pp. 1-14
- Publication year
- FOR Code(s)
- 0101 Pure Mathematics; 0102 Applied Mathematics
- Absorbtion; CEV model; Euler-Maruyama algorithm; Non-Lipschitz diffusion; Weak convergence
- American Institute of Mathematical Sciences
- Publisher URL
- Copyright © 2011 American Institute of Mathematical Sciences. The accepted manuscript is reproduced in accordance with the copyright policy of the publisher.
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