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Parisian ruin over a finite-time horizon

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Abstract

For a risk process R u (t) = u + ct − X(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.

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Authors and Affiliations

  1. Mathematical Institute, University of Wrocław, Wrocław, 50-384, Poland

    Krzysztof Dębicki

  2. Department of Actuarial Science, University of Lausanne, Lausanne, 1015, Switzerland

    Enkelejd Hashorva & LanPeng Ji

Authors
  1. Krzysztof Dębicki
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  2. Enkelejd Hashorva
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  3. LanPeng Ji
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Correspondence to LanPeng Ji.

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Dębicki, K., Hashorva, E. & Ji, L. Parisian ruin over a finite-time horizon. Sci. China Math. 59, 557–572 (2016). https://doi.org/10.1007/s11425-015-5073-6

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  • DOI: https://doi.org/10.1007/s11425-015-5073-6

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