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

Author

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  • Edita Kizinevič

    (Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania)

  • Jonas Šiaulys

    (Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania)

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.

Suggested Citation

  • Edita Kizinevič & Jonas Šiaulys, 2018. "The Exponential Estimate of the Ultimate Ruin Probability for the Non-Homogeneous Renewal Risk Model," Risks, MDPI, vol. 6(1), pages 1-17, March.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:1:p:20-:d:135300
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    References listed on IDEAS

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    Cited by:

    1. Olena Ragulina & Jonas Šiaulys, 2020. "Upper Bounds and Explicit Formulas for the Ruin Probability in the Risk Model with Stochastic Premiums and a Multi-Layer Dividend Strategy," Mathematics, MDPI, vol. 8(11), pages 1-35, October.
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