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

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