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Analytic properties of infinite-horizon survival probability in a risk model with additional funds


Authors: Yu. S. Mishura, O. Yu. Ragulina and O. M. Stroev
Translated by: V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 91 (2014).
Journal: Theor. Probability and Math. Statist. 91 (2015), 131-143
MSC (2010): Primary 91B30; Secondary 60G51
DOI: https://doi.org/10.1090/tpms/972
Published electronically: February 19, 2016
Previous version of record: Original version posted February 4, 2016
Corrected version of record: Current version corrects error introduced by the translator: The name of one of the co-authors, O. Yu. Ragulina, was omitted.
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a generalization of the classical risk model where an insurance company gets additional funds whenever a claim arrives. We investigate the properties of continuity and differentiability of the infinite-horizon survival probability and derive an integro-differential equation. We find a closed form solution of this equation in the case where the claim sizes and additional funds are exponentially distributed.


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Additional Information

Yu. S. Mishura
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: myus@univ.kiev.ua

O. Yu. Ragulina
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: lena_ragulina@mail.ru

O. M. Stroev
Affiliation: Department of Mathematical Modelling, Faculty for Mathematics and Informatics, Chernivtsi Yuriĭ Fed’kovych National University, Kotsyubynskiĭ Street, 2, Chernivtsi, 58012, Ukraine
Email: o.stroiev@chnu.edu.ua

DOI: https://doi.org/10.1090/tpms/972
Keywords: Risk model, survival probability, continuity and differentiability, integro-differential equation
Received by editor(s): October 9, 2014
Published electronically: February 19, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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