A limit theorem for the time of ruin in a Gaussian ruin problem

Jürg Hüsler and Vladimir Piterbarg ()

Stochastic Processes and their Applications, 2008, vol. 118, issue 11, 2014-2021

Abstract: For certain Gaussian processes X(t) with trend -ct[beta] and variance V2(t), the ruin time is analyzed where the ruin time is defined as the first time point t such that X(t)-ct[beta]>=u. The ruin time is of interest in finance and actuarial subjects. But the ruin time is also of interest in other applications, e.g. in telecommunications where it indicates the first time of an overflow. We derive the asymptotic distribution of the ruin time as u-->[infinity] showing that the limiting distribution depends on the parameters [beta], V(t) and the correlation function of X(t).

Keywords: Gaussian; process; Nonstationary; Locally; stationary; Ruin; Ruin; time; Asymptotic; behavior; Limit; distributions (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (5)

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