On a ruin model with both interclaim times and premiums depending on claim sizes

Li, Zhong; Sendova, Kristina P.

doi:10.1080/03461238.2013.811096

Cited by 15 publications

(9 citation statements)

References 7 publications

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“…almost surely, and, consequently, 1 − ϕ(u) = P sup n 1 η n u = 1 according to expression (19). The first part of Theorem 4 is proven.…”

Section: Proof Of Theoremmentioning

confidence: 79%

“…There are a number of results on the calculation of finite time ruin probability, the probability that W(t) 0 for some t ∈ {1, .., T}, for models with non identically distributed claims. See, for instance, [17][18][19][20][21][22][23][24][25][26] and reference therein. However, there are no results on the calculation of the ultimate time ruin probability, the probability that W(t) 0 for some t ∈ N, and of the ultimate time survival probability, the probability that W(t) > 0 for all t ∈ N, for such a general, nonhomogenous, discrete time risk model.…”

Section: Introductionmentioning

confidence: 99%

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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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“…almost surely, and, consequently, 1 − ϕ(u) = P sup n 1 η n u = 1 according to expression (19). The first part of Theorem 4 is proven.…”

Section: Proof Of Theoremmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 99%

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

Grigutis

Šiaulys

2020

Mathematics

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“…The main part of the known results on the Gerber-Shiu function is related with the Sparre Andersen model and various generalizations of this model. For instance, several cases of the Sparre Andersen model were considered by Dickson and Qazvini (2016), Landriault and Willmot (2008), Li and Garrido (2004), Li and Sendova (2015), Lin et al (2003), Schmidli (1999), Willmot and Dickson (2003). Properties of the Gerber-Shiu function in the risk renewal models perturbed by diffusion were investigated by Chi et al (2010), Tsai (2003), Tsai and Willmot (2002), Xu et al (2014), Zhang and Cheung (2016), Zhang et al (2012Zhang et al ( , 2017bZhang et al ( , 2014.…”

mentioning

confidence: 99%

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

Navickienė¹,

Sprindys²,

Šiaulys³

2018

Informatica

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In this work, the discrete time risk model with two seasons is considered. In such model, the claims repeat with time periods of two units, i.e. claim distributions coincide at all even instants and at all odd instants. Our purpose is to derive an algorithm for calculating the values of the particular case of the Gerber-Shiu discounted penalty function E(e −δT 1 {T <∞}), where T is the time of ruin, and δ is a constant nonnegative force of interest. Theoretical results are illustrated by some numerical examples.

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“…Other authors worked with the claim sizes, which have a common distribution function and not necessarily identically distributed inter-arrival times (see Šiaulys 2015, 2017;Burnecki and Giuricich 2017;Mao et al 2017). Other authors dealt with identically distributed claims and inter-arrival times, but there may be some kind of dependence between them (see Chen and Ng 2007;Huang et al 2017;Constantinescu et al 2016;Liu and Gao 2016;Li and Sendova 2015;Shen et al 2016;Yang and Yuen 2016;Yang and Konstantinides 2015;Yang et al 2014;Wang et al 2013). Some authors consider models in which claim amounts are divided in several lines by supposing some dependence relations between these lines (see Fu and Ng 2017;Guo et al 2017;Yang and Yuen 2016).…”

Section: Introductionmentioning

confidence: 99%

The Exponential Estimate of the Ultimate Ruin Probability for the Non-Homogeneous Renewal Risk Model

Kizinevič

Šiaulys

2018

Risks

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In this work, the non-homogeneous risk model is considered. In such a model, claims and inter-arrival times are independent but possibly non-identically distributed. The easily verifiable conditions are found such that the ultimate ruin probability of the model satisfies the exponential estimate exp{− u} for all values of the initial surplus u 0. Algorithms to estimate the positive constant are also presented. In fact, these algorithms are the main contribution of this work. Sharpness of the derived inequalities is illustrated by several numerical examples.

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On a ruin model with both interclaim times and premiums depending on claim sizes

Cited by 15 publications

References 7 publications

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

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

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

The Exponential Estimate of the Ultimate Ruin Probability for the Non-Homogeneous Renewal Risk Model

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