A cyclic approach on classical ruin model

Fei Lung Yuen, Wing Yan Lee and Derrick W.H. Fung

Insurance: Mathematics and Economics, 2020, vol. 91, issue C, 104-110

Abstract: The ruin problem has long since received much attention in the literature. Under the classical compound Poisson risk model, elegant results have been obtained in the past few decades. We revisit the finite-time ruin probability by using the idea of cycle lemma, which was used in proving the ballot theorem. The finite-time result is then extended to infinite-time horizon by applying the weak law of large numbers. The cycle lemma also motivates us to study the claim instants retrospectively, and this idea can be used to reach the ladder height distribution on the infinite-time horizon. The new proofs in this paper link the classical finite-time and infinite-time ruin results, and give an intuitive way to understand the nature of ruin.

Keywords: Ballot theorem; Ruin probability; Stationary and independent increment; Law of large numbers; Deficit at ruin (search for similar items in EconPapers)
JEL-codes: G22 (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:91:y:2020:i:c:p:104-110

DOI: 10.1016/j.insmatheco.2020.01.005

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