On a discrete risk model with two-sided jumps

Abstract

a b s t r a c tIn this paper, we consider a discrete renewal risk model with phase-type interarrival times and two-sided jumps. In this model, downward jumps represent claim loss, while upward jumps are also allowed to represent random gains. Assume that the downward jumps have an arbitrary probability function and the upward jumps have a rational probability generating function. We study the (Gerber-Shiu) discounted penalty function. The generating function, the recursive formula as well as an explicit expression for the discounted penalty function are obtained.

On the Study of Ruin at Two Sided Risk Renewal Processes

“…Substantial amount of works has been devoted to find the various ruin probability components under two sided risk model. For research on this kind of model, we refer to Perry, Stadje and Zacks (2002), Cai and Yang (2005), Yang and Zhimin (2010), Jacobson (2005), Xing, Zhang and Jiang (2008), Zhang, Yang and Li (2010), Albercher, Gerber and Yang (2010), , Dong and Liu (2013) and Korolev, Chertok and Korchagin (2015). In Rebello, J.J and Thampi, K.K (2017) discussed the distribution of time of the ruin, the surplus immediately before ruin and deficit at ruin under two sided risk renewal process using Lindley distribution and others.…”