On a dual model with a dividend threshold

Ng, Andrew

doi:10.1016/j.insmatheco.2008.11.011

Cited by 83 publications

(58 citation statements)

References 15 publications

(23 reference statements)

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“…116-119], and Grandell [33, p.8]. Under such a case, Avanzi et al [9,8], Cheung and Drekic [16], Gerber and Smith [32] and Ng [44] have recently studied dividend problems under a barrier or threshold dividend strategy; whereas Landriault and Sendova [37] considered the case in Remark 1. Markovian arrival process (MAP) is very well documented in the literature of applied probability (e.g.…”

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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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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“…Higher moments have also been considered. See Avanzi et al (2007), Avanzi and Gerber (2008), Cheung and Drekic (2008), Gerber and Smith (2008), Ng (2009) and Ng (2010). Yang and Zhu (2008) compute bounds for the ruin probability.…”

Section: Introductionmentioning

confidence: 99%

Dividend problems in the dual risk model

Afonso

Cardoso

Reis

2013

Insurance: Mathematics and Economics

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“…Applying Dynkin's formula to − ( ), and after the same discussion as of Theorem 1, we also can obtain (13) and (14). Substituting (17) into (13) and 14, we get…”

Section: Theorem 2 the Function 2 ( ) = [ − +mentioning

confidence: 99%

“…We consider the company pays dividends according to the threshold dividend strategy; that is, dividends are paid at a constant rate whenever the modified surplus is above the threshold , and no dividends are paid whenever the modified surplus is below . For recent publications on threshold strategy, see, for example, [3,16,17]. We define the modified risk process by…”

Section: Applications To Dividend Value Functionmentioning

confidence: 99%

The Exit Time and the Dividend Value Function for One-Dimensional Diffusion Processes

Yin

Zhou

2013

Abstract and Applied Analysis

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We investigate the exit times from an interval for a general one-dimensional time-homogeneous diffusion process and their applications to the dividend problem in risk theory. Specifically, we first use Dynkin’s formula to derive the ordinary differential equations satisfied by the Laplace transform of the exit times. Then, as some examples, we solve the closed-form expression of the Laplace transform of the exit times for several popular diffusions, which are commonly used in modelling of finance and insurance market. Most interestingly, as the applications of the exit times, we create the connect between the dividend value function and the Laplace transform of the exit times. Both the barrier and threshold dividend value function are clearly expressed in terms of the Laplace transform of the exit times.

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On a dual model with a dividend threshold

Cited by 83 publications

References 15 publications

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

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

Dividend problems in the dual risk model

The Exit Time and the Dividend Value Function for One-Dimensional Diffusion Processes

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