A note on ruin problems in perturbed classical risk models

Abstract

Abstract. In this short note, we derive explicit formulas for the joint densities of the time to ruin and the number of claims until ruin in perturbed classical risk models, by constructing several auxiliary random processes.

The Exponential Estimate of the Ultimate Ruin Probability for the Non-Homogeneous Renewal Risk Model

“…These assumptions would allow analysis of the model in more realistic cases of insurance. The main results of this paper extend and complement the results of other authors, who have considered the exponential estimate of the ruin probability in the non-homogeneous renewal risk model (see Andrulytė et al 2015;Kievinaitė and Šiaulys 2018;Castañer et al 2013;Grandell and Schmidli 2011;Liu et al 2017a).…”

“…Theorem 4 has the classical form of Lundberg's inequality. Inequalities of such a form, for risk renewal models having the special structures, are proved by Castañer et al (2013); Grandell and Schmidli (2011) and Liu et al (2017a). It is evident that we need a more explicit expression for sup k∈N Ee h(Z k −pθ k ) to obtain sharp upper exponential bounds for the ruin probability.…”

Gerber-Shiu Metrics for a Bivariate Perturbed Risk Process

“…Li et al (2019) studies the finite-time expected discounted penalty function (Gerber-Shiu) for the Cramér-Lundberg model with perturbations by solving a second-order partial integro-differential equation with boundary conditions. For the same model, Liu et al (2017) considers the joint distribution of the time to ruin and the number of claims until ruin. In Su et al (2019), approximations are developed using a Laguerre series expansion; see also Su and Wang (2021).…”