Structural properties of Gerber–Shiu functions in dependent Sparre Andersen models

Cheung, Eric C.K.; Landriault, David; Willmot, Gordon E.; Woo, Jae-Kyung

doi:10.1016/j.insmatheco.2009.05.009

Cited by 62 publications

(72 citation statements)

References 18 publications

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“…A similar result is obtained for the function H(t, y) = F (t) × G(y|t), F (t) = 1 − e −λt , G(y|t) = e −βt G 1 (y) + (1 − e −βt )G 2 (y), which was used in Cheung et al (2010), assuming 1−G 1 (x) < e −dx and 1 − G 2 (x) < e −dx . To get the result we did not use the special exponential form of the function F (t).…”

Section: The Exponential Convergence Of the Gerber-shiu Functionsupporting

confidence: 69%

Mathematical investigation of the Gerber–Shiu function in the case of dependent inter-claim time and claim size

Mihálykó

2011

Insurance: Mathematics and Economics

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Section: The Exponential Convergence Of the Gerber-shiu Functionsupporting

confidence: 69%

Mathematical investigation of the Gerber–Shiu function in the case of dependent inter-claim time and claim size

Mihálykó

2011

Insurance: Mathematics and Economics

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“…In this regard, various researchers (see e.g. Biffis and Morales [11], Cheung and Landriault [19] and Cheung et al [21,22]) have attempted to incorporate various random variables defined before ruin into the Gerber-Shiu function to gain additional insights, albeit in the insurance context. In the present dual model, we also consider the surplus level immediately after the last gain before ruin, namely UðT Nðs U Þ Þ which is given by…”

Section: Introductionmentioning

confidence: 99%

On a Gerber–Shiu type function and its applications in a dual semi-Markovian risk model

Liu

Cheung

2014

Applied Mathematics and Computation

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a b s t r a c tIn this paper, we consider a dual risk process which can be used to model the surplus of a business that invests money constantly and earns gains randomly in both time and amount. The occurrences of the gains and their amounts are assumed follow a semiMarkovian structure (e.g. Reinhard, 1984). We analyze a quantity resembling the Gerber-Shiu expected discounted penalty function (Gerber and Shiu, 1998) that incorporates random variables defined before and after the time of ruin, such as the minimum surplus level before ruin and the time of the first gain after ruin. General properties of the function are studied, and some exact results are derived upon exponential distributional assumptions on either the inter-arrival times or the gain amounts. Applications in a perpetual insurance and the last inter-arrival time containing the time of ruin are given along with some numerical examples.

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“…Such a structurization allows for possible dependence between interclaim times and claim sizes in Sparre Andersen models (e.g., see Cheung et al [9]). …”

Section: Model Description and Assumptionsmentioning

confidence: 99%

Ruin Analysis of a Discrete-Time Dependent Sparre Andersen Model with External Financial Activities and Randomized Dividends

Kim

Drekic

2016

Risks

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Abstract:We consider a discrete-time dependent Sparre Andersen risk model which incorporates multiple threshold levels characterizing an insurer's minimal capital requirement, dividend paying situations, and external financial activities. We focus on the development of a recursive computational procedure to calculate the finite-time ruin probabilities and expected total discounted dividends paid prior to ruin associated with this model. We investigate several numerical examples and make some observations concerning the impact our threshold levels have on the finite-time ruin probabilities and expected total discounted dividends paid prior to ruin.

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Structural properties of Gerber–Shiu functions in dependent Sparre Andersen models

Cited by 62 publications

References 18 publications

Mathematical investigation of the Gerber–Shiu function in the case of dependent inter-claim time and claim size

Mathematical investigation of the Gerber–Shiu function in the case of dependent inter-claim time and claim size

On a Gerber–Shiu type function and its applications in a dual semi-Markovian risk model

Ruin Analysis of a Discrete-Time Dependent Sparre Andersen Model with External Financial Activities and Randomized Dividends

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