Panda G.Banik A.D.Chaudhry M.L.2025-02-172018http://dx.doi.org/10.1007/978-981-10-7814-9_6https://idr.iitbbs.ac.in/handle/2008/2063In this paper, we analyze an insurance risk model wherein the arrival of claims and their sizes occur as renewal processes. Using the duality relation in queueing theory and roots method, we derive closed-form expressions for the ultimate ruin probability, the distribution of the deficit at the time of ruin, and the expected time to ruin in terms of the roots of the characteristic equation. Finally, some numerical computations are portrayed with the help of tables. � 2018, Springer Nature Singapore Pte Ltd.enDeficit at the time of ruinDualityGI/G/1 queuePad� approximationRisk processesRuin probabilityTime to ruinConference Paper