A unified approach to ruin probabilities with delays for spectrally negative Lévy processes

Lkabous, Mohamed Amine; Renaud, Jean‐François

doi:10.1080/03461238.2019.1598890

Cited by 8 publications

(3 citation statements)

References 12 publications

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“…It is known that (see e.g. Equation ( 16) in [11]), for x ≤ a, E x e −qτ + a 1 {τ + a <κ p } = Z q (x, Φ(p + q)) Z q (a, Φ(p + q)) .…”

Section: Verification Lemma and Proof Of The Main Resultsmentioning

confidence: 99%

De Finetti’s Control Problem with Parisian Ruin for Spectrally Negative Lévy Processes

Renaud

2019

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We consider de Finetti's stochastic control problem when the (controlled) process is allowed to spend time under the critical level. More precisely, we consider a generalized version of this control problem in a spectrally negative Lévy model with exponential Parisian ruin. We show that, under mild assumptions on the Lévy measure, an optimal strategy is formed by a barrier strategy and that this optimal barrier level is always less than the optimal barrier level when classical ruin is implemented. Also, we give necessary and sufficient conditions for the barrier strategy at level zero to be optimal.

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“…It is known that (see e.g. Equation ( 16) in [11]), for x ≤ a, E x e −qτ + a 1 {τ + a <κ p } = Z q (x, Φ(p + q)) Z q (a, Φ(p + q)) .…”

Section: Verification Lemma and Proof Of The Main Resultsmentioning

confidence: 99%

De Finetti’s Control Problem with Parisian Ruin for Spectrally Negative Lévy Processes

Renaud

2019

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“…Landriault, Renaud, and Zhou [12], Baurdoux et al [5], and Landriault, Li, and Lkabous [11], who studied exponential Parisian ruin, relied on probabilistic analysis of the so-called scale functions. Lkabous and Renaud [14] also relied on scale functions to analyze a model that combines deterministic and exponential Parisian ruin. Instead, we use comparison methods in integro-differential equations to study the (discounted) probability of exponential Parisian ruin.…”

Section: Introductionmentioning

confidence: 99%

Discounted probability of exponential parisian ruin: Diffusion approximation

Liang

Young

2022

J. Appl. Probab.

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We analyze the discounted probability of exponential Parisian ruin for the so-called scaled classical Cramér–Lundberg risk model. As in Cohen and Young (2020), we use the comparison method from differential equations to prove that the discounted probability of exponential Parisian ruin for the scaled classical risk model converges to the corresponding discounted probability for its diffusion approximation, and we derive the rate of convergence.

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“…To compute the value of H(0) in (19), we need to specify the distribution of the delay window length. We will consider two special cases.…”

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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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A unified approach to ruin probabilities with delays for spectrally negative Lévy processes

Cited by 8 publications

References 12 publications

De Finetti’s Control Problem with Parisian Ruin for Spectrally Negative Lévy Processes

De Finetti’s Control Problem with Parisian Ruin for Spectrally Negative Lévy Processes

Discounted probability of exponential parisian ruin: Diffusion approximation

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

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