The Gerber–Shiu Discounted Penalty Function for the Bi-Seasonal Discrete Time Risk Model

Navickienė, Olga; Sprindys, Jonas; Šiaulys, Jonas

doi:10.15388/informatica.2018.190

Cited by 5 publications

(6 citation statements)

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“…Our obtained results apparently are similar to previously known non-homogeneous risk models, see [16,22,[27][28][29][30], where certain convolutions of random variables occur and initial values for recurrent formulas are needed. Namely, convolutions of distinct r.v.s generating some discrete time non-homogeneous risk model is the reason for not allowing to easily express ultimate time survival probability.…”

Section: Discussionsupporting

confidence: 89%

Recurrent Sequences Play for Survival Probability of Discrete Time Risk Model

Grigutis

Šiaulys

2020

Symmetry

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In this article we investigate a homogeneous discrete time risk model with a generalized premium income rate which can be any natural number. We derive theorems and give numerical examples for finite and ultimate time survival probability calculation for the mentioned model. Our proved statements for ultimate time survival probability calculation, at some level, are similar to the previously known statements for non-homogeneous risk models, where required initial values of survival probability for some recurrent formulas are gathered by certain limit laws. We also give a simplified proof that a ruin is almost unavoidable with a neutral net profit condition and state several conjectures on a certain type of recurrent matrices non-singularity. All the research done can be interpreted as a possibility that symmetric or asymmetric random walk (r.w.) hits (or not) the line u+κt and that possibility is directly related to the expected value of r.w. generating random variable which might be equal, above or bellow κ.

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Section: Discussionsupporting

confidence: 89%

Recurrent Sequences Play for Survival Probability of Discrete Time Risk Model

Grigutis

Šiaulys

2020

Symmetry

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“…Formula (5) shows how the values of probability we seek to calculate are recursively related. For example, to get a value of ϕ(u + 6) for u = 0, 1, .…”

Section: Let Us Denote I Mmentioning

confidence: 99%

“….} and t ∈ N. The model given in (3), we call the three-risk discrete time model, and our motivation to investigate it is research is done in [2][3][4][5], where discrete time risk models were investigated with the following occurrence order of claims {X, Y, X, Y, . .…”

Section: Introductionmentioning

confidence: 99%

Ultimate Time Survival Probability in Three-Risk Discrete Time Risk Model

Grigutis

Šiaulys

2020

Mathematics

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In this paper, we prove recursive formulas for ultimate time survival probability when three random claims X , Y , Z in the discrete time risk model occur in a special way. Namely, we suppose that claim X occurs at each moment of time t ∈ { 1 , 2 , … } , claim Y additionally occurs at even moments of time t ∈ { 2 , 4 , … } and claim Z additionally occurs at every moment of time, which is a multiple of three t ∈ { 3 , 6 , … } . Under such assumptions, the model that is obtained is called the three-risk discrete time model. Such a model is a particular case of a nonhomogeneous risk renewal model. The sequence of claims has the form { X , X + Y , X + Z , X + Y , X , X + Y + Z , … } . Using the recursive formulas, algorithms were developed to calculate the exact values of survival probabilities for the three-risk discrete time model. The running of algorithms is illustrated via numerical examples.

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“…The topic of risk analysis in various sectors is the most important topic that many researchers are paying attention to these days (Navickiene et al, 2018). The goal of the model is to prevent or reduce the threats of negative financial and non-financial consequences associated with the use of information infrastructures, as well as external factors affecting information infrastructures.…”

Section: Risk Management Descriptionmentioning

confidence: 99%

Information Security Risk Assessment in Critical Infrastructure: A Hybrid MCDM Approach

et al. 2019

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The risk analysis has always been one of the essential procedures for any areas. The majority of security incidents occur because of ignoring risks or their inaccurate assessment. It is especially dangerous for critical infrastructures. Thus, the article is devoted to the description of the developed model of risk assessment for the essential infrastructures. The goal of the model is to provide a reliable method for multifaceted risk assessment of information infrastructure. The purpose of the article is to present a developed model based on integrated MCDM approaches that allow to correctly assess the risks of the critical information infrastructures.

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The Gerber–Shiu Discounted Penalty Function for the Bi-Seasonal Discrete Time Risk Model

Cited by 5 publications

References 50 publications

Recurrent Sequences Play for Survival Probability of Discrete Time Risk Model

Recurrent Sequences Play for Survival Probability of Discrete Time Risk Model

Ultimate Time Survival Probability in Three-Risk Discrete Time Risk Model

Information Security Risk Assessment in Critical Infrastructure: A Hybrid MCDM Approach

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