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Estimates for the probability that Itô processes remain near a path


  • Bally, Vlad
  • Fernández, Begoña
  • Meda, Ana


Let W=(Wi)i[set membership, variant]N be an infinite dimensional Brownian motion and (Xt)t>=0 a continuous adaptedn-dimensional process. Set [tau]R=inf{t:Xt-xt>=Rt}, where xt,t>=0 is a Rn-valued deterministic differentiable curve and Rt>0,t>=0 a time-dependent radius. We assume that, up to [tau]R, the process X solves the following (not necessarily Markov) SDE:. Under local conditions on the coefficients, we obtain lower bounds for P([tau]R>=T) as well as estimates for distribution functions and expectations. These results are discussed in the elliptic and log-normal frameworks. An example of a diffusion process that satisfies the weak Hörmander condition is also given.

Suggested Citation

  • Bally, Vlad & Fernández, Begoña & Meda, Ana, 2011. "Estimates for the probability that Itô processes remain near a path," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 2087-2113, September.
  • Handle: RePEc:eee:spapps:v:121:y:2011:i:9:p:2087-2113

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    References listed on IDEAS

    1. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
    2. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    3. Gourieroux, Christian & Sufana, Razvan, 2010. "Derivative Pricing With Wishart Multivariate Stochastic Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 438-451.
    4. Christa Cuchiero & Damir Filipovi'c & Eberhard Mayerhofer & Josef Teichmann, 2009. "Affine processes on positive semidefinite matrices," Papers 0910.0137,, revised Apr 2011.
    5. Andrea Buraschi & Paolo Porchia & Fabio Trojani, 2010. "Correlation Risk and Optimal Portfolio Choice," Journal of Finance, American Finance Association, vol. 65(1), pages 393-420, February.
    6. José Fonseca & Martino Grasselli & Claudio Tebaldi, 2007. "Option pricing when correlations are stochastic: an analytical framework," Review of Derivatives Research, Springer, vol. 10(2), pages 151-180, May.
    7. Bru, Marie-France, 1989. "Diffusions of perturbed principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 127-136, April.
    8. Martino Grasselli & Claudio Tebaldi, 2008. "Solvable Affine Term Structure Models," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 135-153.
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