On the distribution of classic and some exotic ruin times

Abstract

Abstract The time to ruin has been the primary focus of many ruin-related analyses, mainly due to its significance in the assessment of an insurer’s solvency risk. The finite-time ruin probability and more recently, the t -year deferred ruin probability have drawn considerable attention over the years. Embedded into the expected discounted penalty function (Gerber and Shiu, 1998), the time to ruin has also been jointly analyzed with other ruin-related variables of interest, most notably the deficit at ruin. On the other hand, novel ruin definitions have recently been proposed to incorporate more practical considerations into the assessment of an insurer’s solvency risk, such as observing ruin only at discrete times (e.g., the Poisson-observed ruin time) and recognizing an implementation delay in ruin (e.g., the Parisian ruin time with a deterministic or stochastic clock). In this paper, we first revisit some known finite-time ruin results in the compound Poisson risk process and its perturbed version. Thereafter, we enhance the literature on finite-time ruin problems by carrying a distributional study of some modern ruin times, namely the Poisson observed ruin time and the Parisian ruin time.