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Risks 2018, 6(1), 20; https://doi.org/10.3390/risks6010020

The Exponential Estimate of the Ultimate Ruin Probability for the Non-Homogeneous Renewal Risk Model

Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
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Received: 29 January 2018 / Revised: 1 March 2018 / Accepted: 6 March 2018 / Published: 8 March 2018
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Abstract

In this work, the non-homogeneous risk model is considered. In such a model, claims and inter-arrival times are independent but possibly non-identically distributed. The easily verifiable conditions are found such that the ultimate ruin probability of the model satisfies the exponential estimate exp { ϱ u } for all values of the initial surplus u 0 . Algorithms to estimate the positive constant ϱ are also presented. In fact, these algorithms are the main contribution of this work. Sharpness of the derived inequalities is illustrated by several numerical examples. View Full-Text
Keywords: non-homogeneous model; renewal risk model; ruin probability; net profit condition; Lundberg’s inequality non-homogeneous model; renewal risk model; ruin probability; net profit condition; Lundberg’s inequality
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Kizinevič, E.; Šiaulys, J. The Exponential Estimate of the Ultimate Ruin Probability for the Non-Homogeneous Renewal Risk Model. Risks 2018, 6, 20.

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