On Parisian ruin over a finite-time horizon

Abstract

For a risk process $R_u(t)=u+ct-X(t),t\ge 0$, where $u\ge 0$ is the initial capital, $c>0$ is the premium rate and $X(t),t\ge 0$ is an aggregate claim process, we investigate the probability of the Parisian ruin \[ \mathcal{P}_S(u,T_u)=\mathbb{P}\{\inf_{t\in[0,S]} \sup_{s\in[t,t+T_u]} R_u(s)<0\}, \] with a given positive constant $S$ and a positive measurable function $T_u$. We derive asymptotic expansion of ${\mathcal{P}}_S(u,T_u)$, as $u\to \infty$, for the aggregate claim process $X$ modeled by Gaussian processes. As a by-product, we derive the exact tail asymptotics of the infimum of a standard Brownian motion with drift over a finite-time interval.

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References in corpus (2)

• On the infimum attained by the reflected fractional Brownian motion
• Extremes of Aggregated Dirichlet Risks

Cited by in corpus (5)

• Parisian ruin with power-asymmetric variance near the optimal point with application to many-inputs proportional reinsurance
• On the speed of convergence of discrete Pickands constants to continuous ones
• Sojourn Ruin of a Two-Dimensional Fractional Brownian Motion Risk Process
• The time of ultimate recovery in Gaussian risk model
• Parisian Ruin of the Brownian Motion Risk Model with Constant Force of Interest