On the moments of the time to ruin in dependent Sparre Andersen models with emphasis on Coxian interclaim times

Lee, Wing Yan; Willmot, Gordon E.

doi:10.1016/j.insmatheco.2014.08.003

Cited by 5 publications

(3 citation statements)

References 17 publications

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“…They showed how moments of T u could be found from explicit solutions for a Gerber-Shiu function defined as the Laplace transform of T u , and they also derived general expressions for the mean and variance of T 0 . In a pair of papers, Lee & Willmot (2014, 2016 find expressions satisfied by the moments of the time of ruin in dependent SA models with particular assumptions. Independent models can be retrieved as special cases, and their results provide an alternative method of obtaining some of the explicit results obtained below for ordinary SA models, but not for modified models.…”

Section: Introductionmentioning

confidence: 99%

The moments of the time of ruin in Sparre Andersen risk models

Dickson

2022

Ann. actuar. sci.

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We derive formulae for the moments of the time of ruin in both ordinary and modified Sparre Andersen risk models without specifying either the inter-claim time distribution or the individual claim amount distribution. We illustrate the application of our results in the special case of exponentially distributed claims, as well as for the following ordinary models: the classical risk model, phase-type(2) risk models, and the Erlang( $\mathscr{n}$ ) risk model. We also show how the key quantities for modified models can be found.

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Section: Introductionmentioning

confidence: 99%

The moments of the time of ruin in Sparre Andersen risk models

Dickson

2022

Ann. actuar. sci.

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“…(Zhang and Yang 2011) worked on Gerber-Shiu analysis in a perturbed risk model with dependence between claim sizes and inter-claim times, where they also considered that the compound Poisson risk model is perturbed by a Brownian motion. (Lee and Willmot 2014) worked on the moments of the time to ruin in dependent Sparre Andersen models with emphasis on Coxian inter-claim times.…”

Section: Introductionmentioning

confidence: 99%

Gerber–Shiu Function in a Class of Delayed and Perturbed Risk Model with Dependence

Adékambi

Takouda

2020

Risks

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This paper considers the risk model perturbed by a diffusion process with a time delay in the arrival of the first two claims and takes into account dependence between claim amounts and the claim inter-occurrence times. Assuming that the time arrival of the first claim follows a generalized mixed equilibrium distribution, we derive the integro-differential Equations of the Gerber–Shiu function and its defective renewal equations. For the situation where claim amounts follow exponential distribution, we provide an explicit expression of the Gerber–Shiu function. Numerical examples are provided to illustrate the ruin probability.

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“…Yu et al [32] studied the moment of ruin time under the Markov arrival risk model. The moment of ruin time was introduced in the Gerber-Shiu discounted penalty function by Lee and Willmot [33]; then, they studied this new Gerber-Shiu discounted penalty function Sparre-Andersen risk model [34]. Schmidli [35] considered a new Gerber-Shiu discounted penalty function, which is modified with an additional penalty for reaching a level above the initial capital.…”

Section: Introductionmentioning

confidence: 99%

A Note on a Generalized Gerber–Shiu Discounted Penalty Function for a Compound Poisson Risk Model

Ruan

Song

et al. 2019

Mathematics

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In this paper, we propose a new generalized Gerber–Shiu discounted penalty function for a compound Poisson risk model, which can be used to study the moments of the ruin time. First, by taking derivatives with respect to the original Gerber–Shiu discounted penalty function, we construct a relation between the original Gerber–Shiu discounted penalty function and our new generalized Gerber–Shiu discounted penalty function. Next, we use Laplace transform to derive a defective renewal equation for the generalized Gerber–Shiu discounted penalty function, and give a recursive method for solving the equation. Finally, when the claim amounts obey the exponential distribution, we give some explicit expressions for the generalized Gerber–Shiu discounted penalty function. Numerical illustrations are also given to study the effect of the parameters on the generalized Gerber–Shiu discounted penalty function.

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On the moments of the time to ruin in dependent Sparre Andersen models with emphasis on Coxian interclaim times

Cited by 5 publications

References 17 publications

The moments of the time of ruin in Sparre Andersen risk models

The moments of the time of ruin in Sparre Andersen risk models

Gerber–Shiu Function in a Class of Delayed and Perturbed Risk Model with Dependence

A Note on a Generalized Gerber–Shiu Discounted Penalty Function for a Compound Poisson Risk Model

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