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  1. arXiv:1305.2586 (Published 2013-05-12)

    Tail Asymptotics of Deflated Risks

    E. Hashorva, C. Ling, Z. Peng
    Comments: 21
    Categories: math.PR
    Subjects: 60G70, 62G32, 62G20, 91B30

    Random deflated risk models have been considered in recent literatures. In this paper, we investigate second-order tail behavior of the deflated risk X=RS under the assumptions of second-order regular variation on the survival functions of the risk R and the deflator S. Our findings are applied to approximation of Value at Risk, estimation of small tail probability under random deflation and tail asymptotics of aggregated deflated risk

  2. arXiv:1010.3596 (Published 2010-10-18)

    Volume growth and escape rate of Brownian motion on a complete Riemannian manifold

    Elton P. Hsu, Guangnan Qin
    Comments: Published in at http://dx.doi.org/10.1214/09-AOP519 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
    Journal: Annals of Probability 2010, Vol. 38, No. 4, 1570-1582
    Categories: math.PR

    We give an effective upper escape rate function for Brownian motion on a complete Riemannian manifold in terms of the volume growth of the manifold. An important step in the work is estimating the small tail probability of the crossing time between two concentric geodesic spheres by reflecting Brownian motions on the larger geodesic ball.