Dividend Problem with Parisian Delay for a Spectrally Negative Lévy Risk Process

Czarna, Irmina; Palmowski, Zbigniew

doi:10.1007/s10957-013-0283-y

Cited by 41 publications

(30 citation statements)

References 29 publications

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“…When S = ∞ and X is modelled by a specific class of Lévy processes, exact formulas for P ∞ (u, T ), with T ∈ (0, ∞) are derived in [7,4,26]. See also [5,6,28,3] for some recent developments.…”

mentioning

confidence: 99%

Parisian ruin over a finite-time horizon

Dȩbicki

Hashorva

2015

Sci. China Math.

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For a risk process R u (t) = u + ct − X(t), t ≥ 0, where u ≥ 0 is the initial capital, c > 0 is the premium rate and X(t), t ≥ 0 is an aggregate claim process, we investigate the probability of the Parisianwith a given positive constant S and a positive measurable function T u . We derive asymptotic expansion of P S (u, T u ), as u → ∞, for the aggregate claim process X modeled by Gaussian processes. As a by-product, we derive the exact tail asymptotics of the infimum of a standard Brownian motion with drift over a finite-time interval.

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mentioning

confidence: 99%

Parisian ruin over a finite-time horizon

Dȩbicki

Hashorva

2015

Sci. China Math.

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“…Thus h satisfies (11), and by Theorem 4 we have h ≥ v on (0, ∞). However, h is the value function for the barrier strategy π 0 .…”

Section: Barrier Strategiesmentioning

confidence: 82%

On the Optimal Dividend Problem in the Dual Model with Surplus-Dependent Premiums

Marciniak¹,

Palmowski

2017

J Optim Theory Appl

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This paper concerns the dual risk model, dual to the risk model for insurance applications, where premiums are surplus-dependent. In such a model premiums are regarded as costs, while claims refer to profits. We calculate the mean of the cumulative discounted dividends paid until ruin, if the barrier strategy is applied. We formulate associated Hamilton-Jacobi-Bellman equation and identify sufficient conditions for a barrier strategy to be optimal. Some numerical examples are provided when profits have exponential law.

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“…Proposition 1. Let b * be given by (21) with fixed c 1 , c 2 > 0 and x ≥ 0. If b * ∈ (x, ∞), then b * must be solution of…”

Section: Corollary 1 For K < 1 and A > 0 We Have For Xmentioning

confidence: 99%

“…Wang and Zhou [19] defined a draw-down reflected process which can be used to characterise the risk process with capital injections and solved several fluctuation identities. More recently, Wang and Zhou [20] introduced the concept of draw-down Parisian ruin time for a spectrally negative Lévy risk process and obtained the kth moment of the discounted total dividends paid according to the barrier dividend strategy until the draw-down Parisian ruin time, which generalized a result of Czarna and Palmowski [21]. In addition, Wang and Zhou [7] solved a general draw-down version of De Finetti's optimal dividend problem.…”

Section: Introductionmentioning

confidence: 99%

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A Lévy Risk Model with Ratcheting Dividend Strategy and Historic High-Related Stopping

Zhang

Liu

2020

Mathematical Problems in Engineering

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This paper focuses on the De Finetti’s dividend problem for the spectrally negative Lévy risk process, where the dividend is deducted from the surplus process according to the racheting dividend strategy which was firstly introduced in Albrecher et al. (2018). A major feature of the racheting strategy lies in which the dividend rate never decreases. Unlike the conventional studies, the closed form expression for the expected, accumulated, and discounted dividend payments until the draw-down time (rather than the ruin time) is obtained in terms of the scale functions corresponding to the underlying Lévy process. The optimal barrier for the ratcheting strategy is also studied, where the dividend rate can be increased. Finally, two special cases, where the scale functions are explicitly known, i.e., the Brownian motion with drift and the compound Poisson model, are considered to illustrate the main result.

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Dividend Problem with Parisian Delay for a Spectrally Negative Lévy Risk Process

Cited by 41 publications

References 29 publications

Parisian ruin over a finite-time horizon

Parisian ruin over a finite-time horizon

On the Optimal Dividend Problem in the Dual Model with Surplus-Dependent Premiums

A Lévy Risk Model with Ratcheting Dividend Strategy and Historic High-Related Stopping

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