Absolute ruin in the Ornstein-Uhlenbeck type risk model

Ronnie L. Loeffen and Pierre Patie

Papers from arXiv.org

Abstract: We start by showing that the finite-time absolute ruin probability in the classical risk model with constant interest force can be expressed in terms of the transition probability of a positive Ornstein-Uhlenbeck type process, say X. Our methodology applies to the case when the dynamics of the aggregate claims process is a subordinator. From this expression, we easily deduce necessary and sufficient conditions for the infinite-time absolute ruin to occur. We proceed by showing that, under some technical conditions, the transition density of X admits a spectral type representation involving merely the limiting distribution of the process. As a by-product, we obtain a series expansions for the finite-time absolute ruin probability. On the way, we also derive, for the aforementioned risk process, the Laplace transform of the first-exit time from an interval from above. Finally, we illustrate our results by detailing some examples.

Date: 2010-06
New Economics Papers: this item is included in nep-rmg
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1006.2712

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