Joint distributions of some actuarial random vectors in the compound binomial model

Liu, Guoxin; Zhao, Jiquan

doi:10.1016/j.insmatheco.2006.03.001

Cited by 11 publications

(15 citation statements)

References 10 publications

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“…Dos Reis (2004) gave a revision on compound binomial models and studied some interesting new problems regarding the number of claims up to ruin and the number of claims up to recovery. Liu and Zhao (2007) analyzed joint distributions of some actuarial random vectors regarding the model. Moreover, Lefèvre and Loisel (2008) investigated the finite-time ruin probabilities for some classical risk models, including the compound binomial model.…”

Section: Introductionmentioning

confidence: 99%

On the Compound Binomial Risk Model with Delayed Claims and Randomized Dividends

Wat

Yuen

et al. 2018

Risks

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This paper extends the work of Yuen et al. (2013), who obtained explicit results for the discount-free Gerber-Shiu function for a compound binomial risk model in the presence of delayed claims and a randomized dividend strategy with a zero threshold level. Specifically, we establish a recursion method for computing the Gerber-Shiu expected discounted penalty function, which entails a number of important quantities in ruin theory, within the framework of the compound binomial aggregate claims with delayed by-claims and randomized dividends payable at a non-negative threshold level.

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Section: Introductionmentioning

confidence: 99%

On the Compound Binomial Risk Model with Delayed Claims and Randomized Dividends

Wat

Yuen

et al. 2018

Risks

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“…al. [11], Liu and Zhao [12], Eryilmaz [7], Li and Sendova [10], Tuncel and Tank [19] and Tank and Tuncel [17] have studied some extensions of compound binomial risk model. Stanford and Stroinski [15] calculated …nite time ruin probabilities for phase type claim size by recursive methods.…”

Section: Introductionmentioning

confidence: 99%

Survival probabilities for compound binomial risk model with discrete phase-type claims

Tuncel¹

2016

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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SURVIVAL PROBABILITIES FOR COMPOUND BINOMIAL RISK MODEL WITH DISCRETE PHASE-TYPE CLAIMS ALTAN TUNCELAbstract. Due to having useful properties in approximating to the other distributions and mathematically tractable, phase type distributions are commonly used in actuarial risk theory. Claim occurrence time and individual claim size distributions are modelled by phase type distributions in literature. This paper aims to calculate the survival probabilities of an insurance company under the assumption that compound binomial risk model where the individual claim sizes are distributed as discrete Phase Type distribution.

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“…See, for example, [2,3,8,10] and references therein. Among them, Gerber and Shiu [3] studied the joint distribution of the three important actuarial quantities: the time of ruin, the surplus immediately before ruin and the deficit at ruin for the compound Poisson model.…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by Gerber and Shiu, Wu and Wang [10] obtained the explicit expression of this joint distribution and the joint distributions of some actuarial random vectors for the same model by virtue of a renewal mass function, which can also be expressed explicitly. Liu and Zhao [8] obtained the explicit expression of this joint distribution and the joint distributions of some actuarial random vectors for the compound binomial model.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we obtain the explicit expressions of the finite-horizon ruin probability and the definite-horizon ruin probability for the compound negative binomial model, and derive the corresponding joint distributions in the compound negative binomial model along the same lines in [8] and [10]. The rest of the paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

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Ruin probability and joint distributions of some actuarial random vectors in the compound pascal model

Geng

Wan

2010

Acta Math. Appl. Sin. Engl. Ser.

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The compound negative binomial model, introduced in this paper, is a discrete time version. We discuss the Markov properties of the surplus process, and study the ruin probability and the joint distributions of actuarial random vectors in this model. By the strong Markov property and the mass function of a defective renewal sequence, we obtain the explicit expressions of the ruin probability, the finite-horizon ruin probability, the joint distributions of T, U(T − 1), |U (T )| and inf 0≤n<τ 1 U (n) (i.e., the time of ruin, the surplus immediately before ruin, the deficit at ruin and maximal deficit from ruin to recovery) and the distributions of some actuarial random vectors.

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Joint distributions of some actuarial random vectors in the compound binomial model

Cited by 11 publications

References 10 publications

On the Compound Binomial Risk Model with Delayed Claims and Randomized Dividends

On the Compound Binomial Risk Model with Delayed Claims and Randomized Dividends

Survival probabilities for compound binomial risk model with discrete phase-type claims

Ruin probability and joint distributions of some actuarial random vectors in the compound pascal model

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