On the Discounted Penalty Function in a Perturbed Erlang Renewal Risk Model With Dependence

On a Perturbed Risk Model with Time-Dependent Claim Sizes

“…For the perturbed risk model (1), Zhang and Yang [6] used the FGM copula to defne the dependence structure and derived the integro-diferential equations and the Laplace transforms for the Gerber-Shiu functions. Adékambi and Takouda [7] generalized the results of Zhang and Yang [6] by studying the unifed ruin-related measure, in which the claim inter-occurrences follow an Erlang (n) distribution. Recently, the authors of [8,9] investigated (1) with a time delay in the arrival of the frst two claims.…”

Joint Moments of Surplus Immediately Before Ruin and Deficit at Ruin in the Renewal Risk Model

“…[7] introduced the expected discounted penalty function (referred to as the Gerber-Shiu function), which is used to analyze other functions related to the ruin event. Since then, the Gerber-Shiu function has become a unified tool for determining the quantities associated with ruin, and a large number of ruin theory studies have been devoted to the Gerber-Shiu function, which has been widely studied and extended to different surplus processes (see, e.g., [8][9][10][11]). The renewal risk model allows for a more general distribution of the interclaim time, and several researchers have contributed to the analysis of the Sparre Andersen risk model by studying the Gerber-Shiu function (see, e.g., [9,10]).…”