On the dual risk model with tax payments

Albrecher, Hansjörg; Badescu, Andrei L.; Landriault, David

doi:10.1016/j.insmatheco.2008.02.001

Cited by 70 publications

(64 citation statements)

References 7 publications

(8 reference statements)

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“…For example, Yao et al (2011) consider the dividend payments and capital injections control problem in a dual risk model. Further contributions in this strand of literature include Albrecher et al (2008), Avanzi et al (2007), Bayraktar and Egami (2008), Dai et al (2010), Dong and Liu (2010), Wen (2011) and Yang and Sendova (2014).…”

Section: S(t)mentioning

confidence: 99%

On finite-time ruin probabilities in a generalized dual risk model with dependence

Dimitrova

Kaishev

Zhao

2015

European Journal of Operational Research

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Citation: Dimitrova, D. S., Kaishev, V. K. and Zhao, S. (2015). On finite-time ruin probabilities in a generalized dual risk model with dependence. European Journal of Operational Research, 242(1), pp. 134-148. doi: 10.1016Research, 242(1), pp. 134-148. doi: 10. /j.ejor.2014 This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent AbstractIn this paper, we study the finite-time ruin probability in a reasonably generalized dual risk model, where we assume any non-negative non-decreasing cumulative operational cost function and arbitrary capital gains arrival process. Establishing an enlightening link between this dual risk model and its corresponding insurance risk model, explicit expressions for the finite-time survival probability in the dual risk model are obtained under various general assumptions for the distribution of the capital gains. In order to make the model more realistic and general, different dependence structures among capital gains and inter-arrival times and between both are also introduced and corresponding ruin probability expressions are also given. The concept of alarm time, as introduced in Das and Kratz (2012), is applied to the dual risk model within the context of risk capital allocation. Extensive numerical illustrations are provided.

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Section: S(t)mentioning

confidence: 99%

On finite-time ruin probabilities in a generalized dual risk model with dependence

Dimitrova

Kaishev

Zhao

2015

European Journal of Operational Research

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“…the total discounted tax payments before ruin) have since been analyzed in other risk models. For instance, Albrecher et al (2008a) showed that the tax identity (1.5) with minor adjustments remains valid in a dual risk model with exponentially distributed innovations. Wei (2009) examined a compound Poisson risk model with credit interest and showed that Eq.…”

Section: Du (T) = C (U (T)) 1 − γ U (T) I U (T) = U (T) Dt − Ds(t) Tmentioning

confidence: 99%

On a Risk Model with Surplus-dependent Premium and Tax Rates

Cheung

Landriault

2010

Methodol Comput Appl Probab

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In this paper, the compound Poisson risk model with surplus-dependent premium rate is analyzed in the taxation system proposed by Albrecher and Hipp (Blätter der DGVFM 28(1): [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] 2007). In the compound Poisson risk model, Albrecher and Hipp (Blätter der DGVFM 28(1): [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] 2007) showed that a simple relationship between the ruin probabilities in the risk model with and without tax exists. This so-called tax identity was later generalized to a surplus-dependent tax rate by Albrecher et al. (Insur Math Econ 44(2):304-306, 2009). The present paper further generalizes these results to the Gerber-Shiu function with a generalized penalty function involving the maximum surplus prior to ruin. We show that this generalized Gerber-Shiu function in the risk model with tax is closely related to the 'original' Gerber-Shiu function in the risk model without tax defined in a dividend barrier framework. The moments of the discounted tax payments before ruin and the optimal threshold level for the tax authority to start collecting tax payments are also examined.

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“…We refer e.g. to Avanzi et al [4], Gerber and Smith [21], Albrecher et al [2], Dai et al [13], Cheung [11], Afonso et al [1], and Bergel et al [7]. First-passage problems and ruin time are also much studied; see e.g.…”

Section: Introductionmentioning

confidence: 99%

Duality in ruin problems for ordered risk models

Goffard

Lefèvre

2018

Insurance: Mathematics and Economics

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On one hand, an ordered dual risk model is considered where the profit arrivals are governed by an order statistic point process (OSPP). First, the ruin time distribution is obtained in terms of Abel-Gontcharov polynomials. Then, by duality, the ruin time distribution is deduced for an insurance model where the claim amounts correspond to the inter-arrival times in an OSPP. On the other hand, an ordered insurance model is considered with an OSPP as claim arrival process. Lefèvre and Picard [28] determined the finite-time ruin probability in terms of Appell polynomials. Duality is used to derive the ruin probability in a dual model where the profit sizes correspond to the inter-arrival times of an OSPP.MSC 2010: 60G55, 60G40, 12E10.

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On the dual risk model with tax payments

Cited by 70 publications

References 7 publications

On finite-time ruin probabilities in a generalized dual risk model with dependence

On finite-time ruin probabilities in a generalized dual risk model with dependence

On a Risk Model with Surplus-dependent Premium and Tax Rates

Duality in ruin problems for ordered risk models

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