Some ruin theory components of two sided jump problems under renewal risk process

Abstract

In the insurance literature, the Lundberg-Cramer model and Sparre-Anderson model have been discussed to a great extent. A general assumption is that the premium rate is constant over time. But such assumption does not reflect the randomness of the income procured.To describe the stochastic nature, later on many researchers have studied risk models with varying premium, with interest force etc. In this paper we consider the variability of income in two ways both positive and negative .we investigate risk model with random gain (positive jump) and claim amount(negative jump) under a renewal risk process with some assumptions. Explicit expressions for ruin/survival probability, severity of ruin, Barrier probability is also discussed.

On the formulation of a stochastic model for an accumulated claim amount under renewal risk process

“…Robertson (1992) [19] contributed an application of the fast Fourier transform to the computation of aggregate loss distribution. Bortolosso et al [20] , Rebello et al (2017) [14] considered the time to ruin or its Laplace transforms for the renewal risk model, where both the claim inter arrival time distribution and the claim size distribution are Phase types. In 2021, Zhang Lili discussed The Erlangian (n) risk model with two sided jumps and a constant dividend barrier.…”