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

Marciniak, Ewa; Palmowski, Zbigniew

doi:10.1007/s10957-016-1050-7

Cited by 9 publications

(5 citation statements)

References 25 publications

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“…We focus on the dual model (or the spectrally positive Lévy model), which is known to be an appropriate model for a company driven by inventions or discoveries (see, e.g. [3,4,5,9,10,20,21,23,25]). In this context, Avanzi et al [6] solved the case with i.i.d.…”

Section: Introductionmentioning

confidence: 99%

On the optimality of periodic barrier strategies for a spectrally positive Lévy process

Pérez

Yamazaki

2017

Insurance: Mathematics and Economics

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ABSTRACT. We study the optimal dividend problem in the dual model where dividend payments can only be made at the jump times of an independent Poisson process. In this context, Avanzi et al. [6] solved the case with i.i.d. hyperexponential jumps; they showed the optimality of a (periodic) barrier strategy where dividends are paid at dividend-decision times if and only if the surplus is above some level. In this paper, we generalize the results for a general spectrally positive Lévy process with additional terminal payoff/penalty at ruin, and also solve the case with classical bail-outs so that the surplus is restricted to be nonnegative.The optimal strategies as well as the value functions are concisely written in terms of the scale function.Numerical results are also given.AMS 2010 Subject Classifications: 60G51, 93E20, 91B30 JEL Classifications: C44, C61, G24, G32, G35

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Section: Introductionmentioning

confidence: 99%

On the optimality of periodic barrier strategies for a spectrally positive Lévy process

Pérez

Yamazaki

2017

Insurance: Mathematics and Economics

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“…Albrecher et al [2] examine a dual risk model in the presence of tax payments. Marciniak and Palmowski [18] consider a more general dual risk process where the rate of the costs depends on the present amount of reserves. Boxma and Frostig [9] consider the time to ruin and the expected discounted dividends for a different dividend policy, where a certain part of the gain is paid as dividends if upon arrival the gain finds the surplus above a barrier b or if it would bring the surplus above that level.…”

Section: Introductionmentioning

confidence: 99%

A dual risk model with additive and proportional gains: ruin probability and dividends

Boxma

Frostig

Palmowski³

2023

Adv. Appl. Probab.

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We consider a dual risk model with constant expense rate and i.i.d. exponentially distributed gains $C_i$ ( $i=1,2,\dots$ ) that arrive according to a renewal process with general interarrival times. We add to this classical dual risk model the proportional gain feature; that is, if the surplus process just before the ith arrival is at level u, then for $a>0$ the capital jumps up to the level $(1+a)u+C_i$ . The ruin probability and the distribution of the time to ruin are determined. We furthermore identify the value of discounted cumulative dividend payments, for the case of a Poisson arrival process of proportional gains. In the dividend calculations, we also consider a random perturbation of our basic risk process modeled by an independent Brownian motion with drift.

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“…Albrecher et al [1] examine a dual risk model in the presence of tax payments. Marciniak and Palmowski [18] consider a more general dual risk process where the rate of the costs depends on the present amount of reserves. Boxma and Frostig [9] consider the time to ruin and the expected discounted dividends for a different dividend policy, where a certain part of the gain is paid as dividends if upon arrival the gain finds the surplus above a barrier b or if it would bring the surplus above that level.…”

Section: Introductionmentioning

confidence: 99%

A dual risk model with additive and proportional gains: ruin probability and dividends

Boxma¹,

Frostig²,

Palmowski³

2020

Preprint

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We consider a dual risk model with constant expense rate and i.i.d. exponentially distributed gains C i (i = 1, 2, . . . ) that arrive according to a renewal process with general interarrival times. We add to this classical dual risk model the proportional gain feature, that is, if the surplus process just before the ith arrival is at level u, then for a > 0 the capital jumps up to the level (1 + a)u + C i . The ruin probability and the distribution of the time to ruin are determined. We furthermore identify the value of discounted cumulative dividend payments, for the case of a Poisson arrival process of proportional gains. In the dividend calculations, we also consider a random perturbation of our basic risk process modeled by an independent Brownian motion with drift.

show abstract

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

Cited by 9 publications

References 25 publications

On the optimality of periodic barrier strategies for a spectrally positive Lévy process

On the optimality of periodic barrier strategies for a spectrally positive Lévy process

A dual risk model with additive and proportional gains: ruin probability and dividends

A dual risk model with additive and proportional gains: ruin probability and dividends

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