On the Joint Analysis of the Total Discounted Payments to Policyholders and Shareholders: Dividend Barrier Strategy

Cheung, Eric C.K.; Li, Haibo; Woo, Jae-Kyung

doi:10.3390/risks3040491

Cited by 11 publications

(11 citation statements)

References 33 publications

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“…Note that the IDEs (2.2) and (2.5) for in the lower layer are the same as those in theorems 1 and 2 in Cheung et al . (2015) concerning the dividend barrier strategy. This is because these IDEs are obtainable by considering an infinitesimal time interval, for which the dynamics of the surplus process are identical as no dividend is payable in the lower layer regardless of whether a barrier or a threshold strategy is implemented.…”

Section: General Resultsmentioning

confidence: 99%

“…Such an observation will allow us to reuse some of the intermediate results in Cheung et al . (2015) in section 3.□…”

Section: General Resultsmentioning

confidence: 99%

“…Therefore, Cheung et al . (2015) proposed an extended version of the Gerber–Shiu function defined as where (with being the set of non-negative integers) are the orders of moments of and . It is assumed that the cost function f (·) satisfies some mild integrability conditions (see Lemmas 2 and 3).…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, we assume δ 1 ≥0, while δ 2 , δ 3 >0 are possibly different forces of interest used to discount dividends and claims for the shareholders and policyholders, respectively. Note that the indicator function does not appear in Cheung et al .’s (2015) definition since they considered a dividend barrier strategy for which ruin occurs almost surely (a.s.). For notational convenience, we shall use the abbreviation for when it does not cause any confusion.…”

Section: Introductionmentioning

confidence: 99%

“…Under a compound Poisson risk model with a dividend barrier, Cheung et al . (2015) applied to find various covariance measures between ruin-related quantities such as the discounted dividends until ruin and the aggregate discounted claims until ruin. Through some numerical examples, they demonstrated that the covariance between the above two random variables may take positive or negative value and gave some interpretations as well.…”

Section: Introductionmentioning

confidence: 99%

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On the joint analysis of the total discounted payments to policyholders and shareholders: threshold dividend strategy

Cheung

2016

Ann. actuar. sci.

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In insurance risk theory, dividend and aggregate claim amount are of great research interest as they represent the insurance company's payments to its shareholders and policyholders, respectively. Since the analyses of these two quantities are performed separately in the literature, the companion paper by Cheung et al. generalised the Gerber-Shiu expected discounted penalty function by further incorporating the moments of the aggregate discounted claims until ruin and the discounted dividends until ruin. While Cheung et al. considered the compound Poisson model with a dividend barrier in which ruin occurs almost surely, the present paper looks at this generalised Gerber-Shiu function under a threshold dividend strategy where the insurer has a positive survival probability. Because the Gerber-Shiu function is only defined for sample paths leading to ruin, we will additionally study the joint moments of the aggregate discounted claims and the discounted dividends without ruin occurring. Some explicit formulas are derived when the individual claim distribution follows a combination of exponentials. Numerical illustrations involving the correlation between aggregate discounted claims and discounted dividends are given. For the case where ruin occurs, we additionally compute the correlations between the time of ruin and the above two quantities.

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Section: General Resultsmentioning

confidence: 99%

“…Such an observation will allow us to reuse some of the intermediate results in Cheung et al . (2015) in section 3.□…”

Section: General Resultsmentioning

confidence: 99%