Parisian Ruin with Erlang Delay and a Lower Bankruptcy Barrier

Frostig, Esther; Keren-Pinhasik, Adva

doi:10.1007/s11009-019-09693-w

Cited by 10 publications

(5 citation statements)

References 10 publications

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“…They also studied a version of the two-sided exit problem "when the first passage time below level zero is substituted by the Parisian ruin time". Frostig and Keren-Pinhasik [12] studied Parisian ruin with an ultimate bankruptcy barrier (as in [7] in the case of deterministic delay) and i.i.d. exponentially (and then Erlang) distributed random delays.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Parisian ruin with random deficit-dependent delays for spectrally negative Lévy processes

Nguyen¹,

Borovkov²

2021

Preprint

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We consider an interesting natural extension to the Parisian ruin problem under the assumption that the risk reserve dynamics are given by a spectrally negative Lévy process. The distinctive feature of this extension is that the distribution of the random implementation delay windows' lengths can depend on the deficit at the epochs when the risk reserve process turns negative, starting a new negative excursion. This includes the possibility of an immediate ruin when the deficit hits a certain subset. In this general setting, we derive a closed-from expression for the Parisian ruin probability and the joint Laplace transform of the Parisian ruin time and the deficit at ruin.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Parisian ruin with random deficit-dependent delays for spectrally negative Lévy processes

Nguyen¹,

Borovkov²

2021

Preprint

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“…Such type of Parisian ruin has already been studied for Lévy insurance risk models (see, e.g. Albrecher and Ivanovs [1], Landriault et al [14] and Frostig and Keren-Pinhasik [6]). However, in contrast to Parisian ruin in (4), the relationship in Equation (3) does not hold any more when the delay follows an Erlang-distributed implementation delays.…”

Section: Introductionmentioning

confidence: 99%

Poissonian occupation times of spectrally negative Lévy processes with applications

Lkabous

2021

Scandinavian Actuarial Journal

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In this paper, we introduce the concept of Poissonian occupation times below level 0 of a spectrally negative Lévy process. In this case, occupation time is accumulated only when the process is observed to be negative at arrival epochs of an independent Poisson process. Our results extend some well known continuously observed quantities involving occupation times of spectrally negative Lévy processes. As an application, we establish a link between Poissonian occupation times and insurance risk models with Parisian implementation delays. τ + b ,λ and, as a consequence, we examine the Laplace transform as well as the distribution of Poissonian occupation time over an innitetime horizon, that is, O X ∞,λ = n∈N + (τ + 0 • θ ξn )1 {Xξ n <0} .

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“…The Parisian-ruin-related dividend optimization problem was investigated in [10], where the barrier dividend strategy turned out to be the optimal strategy. Work on a variant of the above model in which the duration r is random can be found Draw-down Parisian ruin 1165 in [17], [2], and [14]. Recent work concerning the Parisian ruin with an ultimate bankruptcy level can be found in [8], [11], and [6].…”

Section: Introductionmentioning

confidence: 99%

Draw-down Parisian ruin for spectrally negative Lévy processes

Wang

Zhou²

2020

Adv. Appl. Probab.

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Draw-down time for a stochastic process is the first passage time of a draw-down level that depends on the previous maximum of the process. In this paper we study the draw-down-related Parisian ruin problem for spectrally negative Lévy risk processes. Intuitively, a draw-down Parisian ruin occurs when the surplus process has continuously stayed below the dynamic draw-down level for a fixed amount of time. We introduce the draw-down Parisian ruin time and solve the corresponding two-sided exit problems via excursion theory. We also find an expression for the potential measure for the process killed at the draw-down Parisian time. As applications, we obtain new results for spectrally negative Lévy risk processes with dividend barrier and with Parisian ruin.

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Parisian Ruin with Erlang Delay and a Lower Bankruptcy Barrier

Cited by 10 publications

References 10 publications

Parisian ruin with random deficit-dependent delays for spectrally negative Lévy processes

Parisian ruin with random deficit-dependent delays for spectrally negative Lévy processes

Poissonian occupation times of spectrally negative Lévy processes with applications

Draw-down Parisian ruin for spectrally negative Lévy processes

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