Upper Bounds and Explicit Formulas for the Ruin Probability in the Risk Model with Stochastic Premiums and a Multi-Layer Dividend Strategy

Upper Bounds and Explicit Formulas for the Ruin Probability in the Risk Model with Stochastic Premiums and a Multi-Layer Dividend Strategy

This paper is devoted to the investigation of the ruin probability in the risk model with stochastic premiums where dividends are paid according to a multi-layer dividend strategy. We obtain an exponential bound for the ruin probability and investigate conditions, under which it holds for a number o...

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Main Authors: Olena Ragulina, Jonas Šiaulys
Format: Article
Language:English
Published: MDPI AG 2020-10-01
Series:Mathematics
Subjects:
risk model
stochastic premiums
ruin probability
net profit condition
multi-layer dividend strategy
constant dividend strategy
Online Access:https://www.mdpi.com/2227-7390/8/11/1885
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spelling doaj-ed101913f0c44a7f9408bb00f06d21242020-11-25T04:00:46ZengMDPI AGMathematics2227-73902020-10-0181885188510.3390/math8111885Upper Bounds and Explicit Formulas for the Ruin Probability in the Risk Model with Stochastic Premiums and a Multi-Layer Dividend StrategyOlena Ragulina0Jonas Šiaulys1Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska Str. 64, 01601 Kyiv, UkraineInstitute of Mathematics, Vilnius University, Naugarduko 24, Vilnius LT-03225, LithuaniaThis paper is devoted to the investigation of the ruin probability in the risk model with stochastic premiums where dividends are paid according to a multi-layer dividend strategy. We obtain an exponential bound for the ruin probability and investigate conditions, under which it holds for a number of distributions of the premium and claim sizes. Next, we use the exponential bound to construct non-exponential bounds for the ruin probability. We show that the non-exponential bounds turn out to be tighter than the exponential one in some cases. Moreover, we derive explicit formulas for the ruin probability when the premium and claim sizes have either the hyperexponential or the Erlang distributions and apply them to investigate how tight the bounds are. To illustrate and analyze the results obtained, we give numerical examples.https://www.mdpi.com/2227-7390/8/11/1885risk modelstochastic premiumsruin probabilitynet profit conditionmulti-layer dividend strategyconstant dividend strategy
collection DOAJ
language English
format Article
sources DOAJ
author Olena Ragulina
Jonas Šiaulys
spellingShingle Olena Ragulina
Jonas Šiaulys
Upper Bounds and Explicit Formulas for the Ruin Probability in the Risk Model with Stochastic Premiums and a Multi-Layer Dividend Strategy
Mathematics
risk model
stochastic premiums
ruin probability
net profit condition
multi-layer dividend strategy
constant dividend strategy
author_facet Olena Ragulina
Jonas Šiaulys
author_sort Olena Ragulina
title Upper Bounds and Explicit Formulas for the Ruin Probability in the Risk Model with Stochastic Premiums and a Multi-Layer Dividend Strategy
title_short Upper Bounds and Explicit Formulas for the Ruin Probability in the Risk Model with Stochastic Premiums and a Multi-Layer Dividend Strategy
title_full Upper Bounds and Explicit Formulas for the Ruin Probability in the Risk Model with Stochastic Premiums and a Multi-Layer Dividend Strategy
title_fullStr Upper Bounds and Explicit Formulas for the Ruin Probability in the Risk Model with Stochastic Premiums and a Multi-Layer Dividend Strategy
title_full_unstemmed Upper Bounds and Explicit Formulas for the Ruin Probability in the Risk Model with Stochastic Premiums and a Multi-Layer Dividend Strategy
title_sort upper bounds and explicit formulas for the ruin probability in the risk model with stochastic premiums and a multi-layer dividend strategy
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2020-10-01
description This paper is devoted to the investigation of the ruin probability in the risk model with stochastic premiums where dividends are paid according to a multi-layer dividend strategy. We obtain an exponential bound for the ruin probability and investigate conditions, under which it holds for a number of distributions of the premium and claim sizes. Next, we use the exponential bound to construct non-exponential bounds for the ruin probability. We show that the non-exponential bounds turn out to be tighter than the exponential one in some cases. Moreover, we derive explicit formulas for the ruin probability when the premium and claim sizes have either the hyperexponential or the Erlang distributions and apply them to investigate how tight the bounds are. To illustrate and analyze the results obtained, we give numerical examples.
topic risk model
stochastic premiums
ruin probability
net profit condition
multi-layer dividend strategy
constant dividend strategy
url https://www.mdpi.com/2227-7390/8/11/1885
work_keys_str_mv AT olenaragulina upperboundsandexplicitformulasfortheruinprobabilityintheriskmodelwithstochasticpremiumsandamultilayerdividendstrategy
AT jonassiaulys upperboundsandexplicitformulasfortheruinprobabilityintheriskmodelwithstochasticpremiumsandamultilayerdividendstrategy
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