The Gerber-Shiu Expected Penalty Function for the Risk Model with Dependence and a Constant Dividend Barrier

Liu, Donghai; Liu, Zaiming; Peng, Dan

doi:10.1155/2014/730174

Cited by 4 publications

(4 citation statements)

References 19 publications

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“…Thus, we get the system of 3k − 1 linear equations (24)- (27) to determine 3k − 1 unknown constants. That system has a unique solution provided that its determinant is not equal to 0.…”

Section: Lemma 1 Let the Surplus Process (X Bmentioning

confidence: 99%

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

Ragulina¹

2019

Modern Stochastics: Theory and Applications

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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

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“…Thus, we get the system of 3k − 1 linear equations (24)- (27) to determine 3k − 1 unknown constants. That system has a unique solution provided that its determinant is not equal to 0.…”

Section: Lemma 1 Let the Surplus Process (X Bmentioning

confidence: 99%

“…Next, from the equality ψ(0) = 1 we get (25). Lastly, substituting (31) into 26) and (27), respectively. Thus, we get the system of 3k − 1 linear equations ( 24)-( 27) to determine 3k − 1 unknown constants.…”

Section: Explicit Formulas For the Ruin Probabilitymentioning

confidence: 99%

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

Ragulina¹

2019

Modern Stochastics: Theory and Applications

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“…They analyze the Gerber-Shiu function and the expected discounted dividend payments and then concentrate on exponentially distributed claim sizes investigating the impact of the dependence on ruin quantities. The same model is studied in [32], where, in particular, the authors show that the solution to the integro-differential equation for the Gerber-Shiu function is a linear combination of the Gerber-Shiu function with no barrier and the solution to the associated homogeneous integro-differential equation. For some earlier results in this direction, see also [26].…”

Section: Introductionmentioning

confidence: 99%

The risk model with stochastic premiums, dependence and a threshold dividend strategy

Ragulina¹

2017

Modern Stoch. Theory Appl.

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The paper deals with a generalization of the risk model with stochastic premiums where dependence structures between claim sizes and inter-claim times as well as premium sizes and inter-premium times are modeled by Farlie-Gumbel-Morgenstern copulas. In addition, dividends are paid to its shareholders according to a threshold dividend strategy. We derive integral and integro-differential equations for the Gerber-Shiu function and the expected discounted dividend payments until ruin. Next, we concentrate on the detailed investigation of the model in the case of exponentially distributed claim and premium sizes. In particular, we find explicit formulas for the ruin probability in the model without either dividend payments or dependence as well as for the expected discounted dividend payments in the model without dependence. Finally, numerical illustrations are presented.

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“…Some other papers thought about the constant dividend too. See Liu and Dan [12] and Zhang Lianzeng and Liu He [13].…”

Section: Introductionmentioning

confidence: 99%

The Risk Model with a Constant Dividend Barrier Affected by a Threshold Value

2022

AJPAS

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This paper considers a new risk model with a constant dividend barrier, which the claim amount affected by a threshold value. The hypothesis of the model is presented and the integro-differential equation for the Gerber-Shiu penalty function is given. Then the linear solution of the Gerber-Shiu discounted penalty function is figured out. The paper also derives the integro-differential equation and the linear solution of the expected discounted dividend payments. An example is given too.

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The Gerber-Shiu Expected Penalty Function for the Risk Model with Dependence and a Constant Dividend Barrier

Cited by 4 publications

References 19 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

The risk model with stochastic premiums, dependence and a threshold dividend strategy

The Risk Model with a Constant Dividend Barrier Affected by a Threshold Value

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