Optimality results for dividend problems in insurance

Albrecher, Hansjörg; Thonhauser, Stefan

doi:10.1007/bf03191909

Cited by 146 publications

(93 citation statements)

References 108 publications

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“…This is a more balanced criterion in that more dividends lead to an earlier ruin, which itself decreases the expected amount of dividends received later. This proposition led to the study of optimal dividend strategies in many actuarial surplus models, see Avanzi (2009) and Albrecher and Thonhauser (2009) for reviews.…”

Section: Motivation and Literature Reviewmentioning

confidence: 99%

On the Interface Between Optimal Periodic and Continuous Dividend Strategies in the Presence of Transaction Costs

Avanzi

Wong

2016

ASTIN Bull.

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In the classical optimal dividends problem, dividend decisions are allowed to be made at any point in time -according to a continuous strategy. Depending on the surplus process that is considered and whether dividend payouts are bounded or not, optimal strategies are generally of a band, barrier or threshold type. In reality, while surpluses change continuously, dividends are generally paid on a periodic basis. Because of this, the actuarial literature has recently considered strategies where dividends are only allowed to be distributed at (random) discrete times -according to a periodic strategy.In this paper, we focus on the Brownian risk model. In this context, the optimal continuous and periodic strategies have previously been shown (independently of one another) to be of barrier type. For the first time, we consider a model where both strategies are used. In such a hybrid strategy, decisions are allowed to be made either at any time (continuously), or periodically at a lower cost. This proves optimal in some cases. We also determine under which combination of parameters a pure continuous, pure periodic or hybrid (including both continuous and periodic dividend payments) barrier strategy is optimal. Interestingly, the hybrid strategy lies in-between periodic and continuous strategies, which provides some interesting insights. Results are illustrated.

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Section: Motivation and Literature Reviewmentioning

confidence: 99%

On the Interface Between Optimal Periodic and Continuous Dividend Strategies in the Presence of Transaction Costs

Avanzi

Wong

2016

ASTIN Bull.

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“…Note that the compound Poisson risk process defined in (1) corresponds to the case γ = c− 1 0 z ν(dz), σ = 0 and ν(dz) = λF (dz), where λ is the jump intensity of N and where F is the distribution of the C i 's, while a Brownian motion risk process corresponds to the case σ > 0 and ν(dz) ≡ 0. It is well known that X has paths of bounded variation if and only if σ = 0 and 1 0 z ν(dz) < ∞.…”

Section: Lévy Insurance Risk Processesmentioning

confidence: 99%

“…Consequently, the objective function under study is closely related to the so-called Dickson and Waters modifications [15]. For more background and literature coverage on dividend strategies and optimal dividends problems in risk theory, we refer the reader to the reviews of Avanzi [5] and Albrecher and Thonhauser [1] respectively.…”

Section: Problem Formulationmentioning

confidence: 99%

De Finetti’s optimal dividends problem with an affine penalty function at ruin

Loeffen

Renaud

2010

Insurance: Mathematics and Economics

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Abstract. In a Lévy insurance risk model, under the assumption that the tail of the Lévy measure is log-convex, we show that either a horizontal barrier strategy or the take-the-money-and-run strategy maximizes, among all admissible strategies, the dividend payments subject to an affine penalty function at ruin. As a key step for the proof, we prove that, under the aforementioned condition on the jump measure, the scale function of the spectrally negative Lévy process has a log-convex derivative.

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“…This was followed by numerous other researchers who further explored the problem in a variety of contexts (for reviews of the area, the interested reader is directed to Albrecher and Thonhauser [2] and Avanzi [3]). In particular, Drekic and Mera [4] considered the ruin analysis of a threshold-based dividend payment strategy in a discrete-time Sparre Andersen model.…”

Section: Introductionmentioning

confidence: 99%

Ruin Analysis of a Discrete-Time Dependent Sparre Andersen Model with External Financial Activities and Randomized Dividends

Kim

Drekic

2016

Risks

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Abstract:We consider a discrete-time dependent Sparre Andersen risk model which incorporates multiple threshold levels characterizing an insurer's minimal capital requirement, dividend paying situations, and external financial activities. We focus on the development of a recursive computational procedure to calculate the finite-time ruin probabilities and expected total discounted dividends paid prior to ruin associated with this model. We investigate several numerical examples and make some observations concerning the impact our threshold levels have on the finite-time ruin probabilities and expected total discounted dividends paid prior to ruin.

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Optimality results for dividend problems in insurance

Cited by 146 publications

References 108 publications

On the Interface Between Optimal Periodic and Continuous Dividend Strategies in the Presence of Transaction Costs

On the Interface Between Optimal Periodic and Continuous Dividend Strategies in the Presence of Transaction Costs

De Finetti’s optimal dividends problem with an affine penalty function at ruin

Ruin Analysis of a Discrete-Time Dependent Sparre Andersen Model with External Financial Activities and Randomized Dividends

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