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Multiseasonal discrete-time risk model revisited

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Abstract

In this work, we set up the distribution function of \(\mathcal{M}:={\mathrm{sup}}_{n\ge 1}{\sum }_{i=1}^{n}\left({X}_{i}-1\right),\) where the random walk \({\sum }_{i=1}^{n}{X}_{i},n\in {\mathbb{N}},\) is generated by N periodically occurring distributions, and the integer-valued and nonnegative random variablesX1,X2, . . . are independent. The considered random walk generates a so-called multiseasonal discrete-time risk model, and a known distribution of random variable M enables us to calculate the ultimate time ruin or survival probability. Verifying obtained theoretical statements, we demonstrate several computational examples for survival probability P(M < u) when N = 2, 3, or 10.

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Authors and Affiliations

  1. Institute of Mathematics, Vilnius University, Naugarduko str. 24, LT-03225, Vilnius, Lithuania

    Andrius Grigutis, Jonas Jankauskas & Jonas Šiaulys

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  1. Andrius Grigutis
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  2. Jonas Jankauskas
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Grigutis, A., Jankauskas, J. & Šiaulys, J. Multiseasonal discrete-time risk model revisited. Lith Math J 63, 466–486 (2023). https://doi.org/10.1007/s10986-023-09613-z

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