Parisian ruin in the dual model with applications to the G/M/1 queue

Frostig, Esther; Keren-Pinhasik, Adva

doi:10.1007/s11134-017-9529-y

Cited by 3 publications

(4 citation statements)

References 24 publications

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“…For this problem, the famous Kendall identity is applicable (see, e.g., Borovkov and Burq [9]). One can check that, as expected, formula (20) is in agreement with that identity.…”

Section: Ordered Dual Risk Modelsupporting

confidence: 81%

“…There exists here a close and important connection with queueing models; see e.g. Frostig [19], Badescu et al [5] and Frostig and KerenPinhasik [20].…”

Section: Introductionmentioning

confidence: 78%

“…(a) Suppose that {M (t), t ≥ 0} is a Poisson process of parameter λ, and that the profit sizes are exponentially distributed of parameter µ. Then, formula (20) becomes explicit as the density part of a compound Poisson distribution with exponentially distributed summands is known (see, e.g., Rolski et al [35], Equation 4.2.8). This yields…”

Section: Ordered Dual Risk Modelmentioning

confidence: 99%

“…Then, M (t) has a geometric distribution with probability of success β/(t + β) (see case (3) in Section 2), and formula (20) gives, after some elementary calculations,…”

Section: Ordered Dual Risk Modelmentioning

confidence: 99%

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Duality in ruin problems for ordered risk models

Goffard

Lefèvre

2018

Insurance: Mathematics and Economics

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On one hand, an ordered dual risk model is considered where the profit arrivals are governed by an order statistic point process (OSPP). First, the ruin time distribution is obtained in terms of Abel-Gontcharov polynomials. Then, by duality, the ruin time distribution is deduced for an insurance model where the claim amounts correspond to the inter-arrival times in an OSPP. On the other hand, an ordered insurance model is considered with an OSPP as claim arrival process. Lefèvre and Picard [28] determined the finite-time ruin probability in terms of Appell polynomials. Duality is used to derive the ruin probability in a dual model where the profit sizes correspond to the inter-arrival times of an OSPP.MSC 2010: 60G55, 60G40, 12E10.

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“…For this problem, the famous Kendall identity is applicable (see, e.g., Borovkov and Burq [9]). One can check that, as expected, formula (20) is in agreement with that identity.…”

Section: Ordered Dual Risk Modelsupporting

confidence: 81%

“…There exists here a close and important connection with queueing models; see e.g. Frostig [19], Badescu et al [5] and Frostig and KerenPinhasik [20].…”

Section: Introductionmentioning

confidence: 78%

Section: Ordered Dual Risk Modelmentioning

confidence: 99%

“…Then, M (t) has a geometric distribution with probability of success β/(t + β) (see case (3) in Section 2), and formula (20) gives, after some elementary calculations,…”

Section: Ordered Dual Risk Modelmentioning

confidence: 99%

See 2 more Smart Citations