Parisian & cumulative Parisian ruin probability for two-dimensional Brownian risk model

Abstract

Parisian ruin probability in the classical Brownian risk model, unlike the standard ruin probability can not be explicitly calculated even in one-dimensional setup. Resorting on asymptotic theory, we derive in this contribution the asymptotic approximations of both Parisian and cumulative Parisian ruin probabilities and simultaneous ruin time for the two-dimensional Brownian risk model when the initial capital increases to infinity.

Keywords:

• Brownian risk model
• Brownian motion
• simultaneous ruin probability
• simultaneous ruin time
• ruin time approximation

AMS Classifications:

• Primary 60G15
• secondary 60G70

Disclosure statement

No potential conflict of interest was reported by the author(s).