The discounted penalty function with multi-layer dividend strategy in the phase-type risk model

Jiang, Wuyuan; Yang, Zhaojun; Xin-ping, LI

doi:10.1016/j.spl.2012.03.012

Cited by 12 publications

(5 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof. Taking into account the notation introduced in Section 2 and applying Lemma 1 we conclude that the function ψ j (x) is a solution to (19)…”

Section: Lemma 1 Let the Surplus Process (X Bmentioning

confidence: 89%

“…Hence, piecewise differential equation ( 19) has a unique solution satisfying certain conditions and that solution is given by ( 23). Since we have derived (19) from (18) without any additional assumptions concerning the differentiability of ψ(x), we conclude that the functions ψ j (x), 1 ≤ j ≤ k, given by ( 23) are unique solutions to (18) on the intervals [b j−1 , b j ] satisfying certain conditions. This guaranties that the functions ψ j (x) we have found coincide with the ruin probability on [b j−1 , b j ], which completes the proof.…”

Section: Explicit Formulas For the Ruin Probabilitymentioning

confidence: 93%

“…Results related to perturbed compound Poisson risk models under multi-layer dividend strategies can be found in [31,42]. In addition, different classes of more general renewal risk models are investigated in [15,19,40,41], and some recent papers deal with risk models that incorporate various dependence structures (see, e.g., [21,38,46,48]).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The risk model with stochastic premiums and a multi-layer dividend strategy

Ragulina¹

2019

Modern Stochastics: Theory and Applications

View full text Add to dashboard Cite

The paper deals with a generalization of the risk model with stochastic premiums where dividends are paid according to a multi-layer dividend strategy. First of all, we derive piecewise integro-differential equations for the Gerber-Shiu function and the expected discounted dividend payments until ruin. In addition, we concentrate on the detailed investigation of the model in the case of exponentially distributed claim and premium sizes and find explicit formulas for the ruin probability as well as for the expected discounted dividend payments. Lastly, numerical illustrations for some multi-layer dividend strategies are presented.Keywords Risk model with stochastic premiums, multi-layer dividend strategy, Gerber-Shiu function, expected discounted dividend payments, ruin probability, piecewise integro-differential equation 2010 MSC 91B30, 60G51

show abstract

“…Proof. Taking into account the notation introduced in Section 2 and applying Lemma 1 we conclude that the function ψ j (x) is a solution to (19)…”

Section: Lemma 1 Let the Surplus Process (X Bmentioning

confidence: 89%

Section: Explicit Formulas For the Ruin Probabilitymentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The risk model with stochastic premiums and a multi-layer dividend strategy

Ragulina¹

2019

Modern Stochastics: Theory and Applications

View full text Add to dashboard Cite

show abstract

“…Following the similar arguments with those in [11], if d i−1 ≤ u < d i , i = 1 2 M, we obtain the following equation for M j u y , j = 1 2 n, by taking into account whether the state associated with the surplus process has changed in a small interval 0 dt or not,…”

Section: Integro-differential System For the Moment Generating Functionmentioning

confidence: 96%

Dividend Payments in a Risk Model Perturbed by Diffusion with Multiple Thresholds

Jiang

Yang

2013

Stochastic Analysis and Applications

Self Cite

View full text Add to dashboard Cite

We consider a perturbed renewal risk model where the interclaim times are phase-type distributed and the dividend payment is a step function depending on the current surplus level. We obtain the integro-differential equations with boundary conditions for the moment-generating functions and the moments of arbitrary order of the present value of all dividend payments until ruin. Explicit expressions for the expected discounted dividend payments are derived if the claim amount distribution belongs to the rational family. Last, we present an example to show how the results are applied.

show abstract

“…Multi-layer dividend strategies are of special interest because they enable to change the intensity of dividend payments depending on the current surplus. Different risk models with multi-layer dividend strategies are investigated in [25][26][27][28][29][30][31][32][33][34][35][36]. In particular, algorithmic schemes for the determination of explicit expressions for the Gerber-Shiu function and the expected discounted dividend payments in the classical risk model with multi-layer dividend strategies are developed in [25].…”

Section: Introductionmentioning

confidence: 99%

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

Ragulina

Šiaulys

2020

Mathematics

View full text Add to dashboard Cite

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.

show abstract

The discounted penalty function with multi-layer dividend strategy in the phase-type risk model

Cited by 12 publications

References 16 publications

The risk model with stochastic premiums and a multi-layer dividend strategy

The risk model with stochastic premiums and a multi-layer dividend strategy

Dividend Payments in a Risk Model Perturbed by Diffusion with Multiple Thresholds

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

Contact Info

Product

Resources

About