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Science China Mathematics

, Volume 59, Issue 3, pp 557–572 | Cite as

Parisian ruin over a finite-time horizon

  • Krzysztof Dębicki
  • Enkelejd Hashorva
  • LanPeng Ji
Articles

Abstract

For a risk process R u (t) = u + ctX(t), t ≥ 0, where u ≥ 0 is the initial capital, c > 0 is the premium rate and X(t), t ≥ 0 is an aggregate claim process, we investigate the probability of the Parisian ruin
$$\mathcal{P}_S (u,T_u ) = \mathbb{P}\left\{ {\mathop {\inf }\limits_{t \in [0,S]} \mathop {\sup }\limits_{s \in [t,t + T_u ]} R_u (s) < 0} \right\}, S,T_u > 0.$$
For X being a general Gaussian process we derive approximations of PS(u, T u ) as u→∞. As a by-product, we obtain the tail asymptotic behaviour of the infimum of a standard Brownian motion with drift over a finite-time interval.

Keywords

Parisian ruin Gaussian process Lévy process fractional Brownian motion infimum of Brownian motion generalized Pickands constant generalized Piterbarg constant 

MSC(2010)

60G15 60G70 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Krzysztof Dębicki
    • 1
  • Enkelejd Hashorva
    • 2
  • LanPeng Ji
    • 2
  1. 1.Mathematical InstituteUniversity of WrocławWrocławPoland
  2. 2.Department of Actuarial ScienceUniversity of LausanneLausanneSwitzerland

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