On the expected discounted penalty function for risk process with tax

Wang, Wenyuan; Ming, Ruixing; Hu, Yijun

doi:10.1016/j.spl.2010.12.012

Cited by 14 publications

(9 citation statements)

References 12 publications

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“…This formula generalizes Theorem 2.1 of Wang et al [23] and may be viewed as an extension of the tax identity, see also Cheung and Landriault [12, (2.16)] and Kyprianou and Zhou [19].…”

Section: Consider the General Gerber-shiu Discounted Penalty Functionsupporting

confidence: 63%

The Tax Identity For Markov Additive Risk Processes

Albrecher

Avram²,

Constantinescu

et al. 2012

Methodol Comput Appl Probab

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Taxed risk processes, i.e. processes which change their drift when reaching new maxima, represent a certain type of generalizations of Lévy and of Markov additive processes (MAP), since the times at which their Markovian mechanism changes are allowed to depend on the current position. In this paper we study generalizations of the tax identity of Albrecher and Hipp [3] from the classical risk model to more general risk processes driven by spectrally-negative MAPs. We use the Sparre Andersen risk processes with phase-type interarrivals to illustrate the ideas in their simplest form.

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“…This formula generalizes Theorem 2.1 of Wang et al [23] and may be viewed as an extension of the tax identity, see also Cheung and Landriault [12, (2.16)] and Kyprianou and Zhou [19].…”

Section: Consider the General Gerber-shiu Discounted Penalty Functionsupporting

confidence: 63%

The Tax Identity For Markov Additive Risk Processes

Albrecher

Avram²,

Constantinescu

et al. 2012

Methodol Comput Appl Probab

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“…Recently, Gerber and Shiu [5] introduced a discounted penalty function with respect to the time of ruin, the surplus immediately before ruin, and the deficit at ruin, which has been proven to be a powerful analytical tool. Some related results can be found in Cheng et al [6], Lin et al [7], Wang and Wu [8], Wang et al [9], and Willmot and Wood [10]. For the compound binomial model, Tan and Yang [11] consider the risk model (1) modified by the inclusion of dividends and derive recursion formulas and an asymptotic estimate for the ruin probability, the probability function of the surplus prior to the ruin time, and the severity of ruin, and so forth.…”

Section: Introductionmentioning

confidence: 94%

Randomized Dividends in a Discrete Insurance Risk Model with Stochastic Premium Income

2013

Mathematical Problems in Engineering

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The compound binomial insurance risk model is extended to the case where the premium income process, based on a binomial process, is no longer a constant premium rate of 1 per period and insurer pays a dividend of 1 with a probabilityq0when the surplus is greater than or equal to a nonnegative integerb. The recursion formulas for expected discounted penalty function are derived. As applications, we present the recursion formulas for the ruin probability, the probability function of the surplus prior to the ruin time, and the severity of ruin. Finally, numerical example is also given to illustrate the effect of the related parameters on the ruin probability.

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“…• Guess in advance that 'W (q) (ξ (x))f (x)/W (q) (ξ (x)) ≥ 1 for all x', which is equivalent to (35), to arrive at a candidate solution (34) to (14). Then we should prove that (34) satisfies 'W (q) (ξ (x))f (x)/W (q) (ξ (x)) ≥ 1 for all x', to guarantee that this candidate solution (34) is indeed a solution to (14).…”

Section: Characterizing the Optimal Return Function And Strategymentioning

confidence: 99%

“…Proposition 6. Suppose that Assumption 1 and condition (35) hold, which is equivalent to a combination of the two cases…”

Section: Proposition 5 Suppose That Assumption 1 and Condition (32) mentioning

confidence: 99%

Optimal loss-carry-forward taxation for Lévy risk processes stopped at general draw-down time

Wang

Zhang

2019

Adv. Appl. Probab.

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in this paper the problem of maximizing the expected accumulated discounted tax payments of an insurance company, whose reserve process (before taxes are deducted) evolves as a spectrally negative Lévy process with the usual exclusion of negative subordinator or deterministic drift. Tax payments are collected according to the very general loss-carryforward tax system introduced in Kyprianou and Zhou (2009). To achieve a balance between taxation optimization and solvency, we consider an interesting modified objective function by considering the expected accumulated discounted tax payments of the company until the general draw-down time, instead of until the classical ruin time. The optimal tax return function together with the optimal tax strategy is derived, and some numerical examples are also provided. processes and the Markove additive processes. In the following, we will summarize the vast loss-carryforward tax concerned literatures which, classified by the problems addressed in these literatures, consists of four components: (1) Gerber-Shiu function; (2) Distribution of the accumulated discounted tax payments; (3) Maximizing the expected accumulated discounted tax payments by delaying starting taxation until the surplus exceeds a critical threshold level; and (4) Finding the optimal tax strategy to maximize the expected accumulated discounted tax payments.With respect to (1), the study concerning loss-carry-forward tax has undergone an impressive metamorphosis. The earliest work of Albrecher and Hipp (2007) found a simple relationship (or, called, tax identity) between the ruin probabilities under the classical compound Poisson risk models with and without constant tax rate. By linking queueing concepts with risk theory, another simple and insightful proof for the tax identity was provided in Albrecher et al. (2009). The tax identity was then extended to the classical compound Poisson risk processes with constant credit interest rate and surplus-dependent tax rate in Wei (2009); to the spectrally negative Lévy risk processes with constant tax rate in Albrecher et al. (2008); to the time-homogeneous diffusion risk processes with surplus-dependent tax rate in Li et al. (2013); and to the Markove additive risk processes with surplus-dependent tax rate in Albrecher et al. (2014). Full form of Gerber-Shiu functions was derived by Wang et al. (2011) in the classical compound Poisson risk model with a constant tax rate; by Ming et al. (2010) in the classical compound Poisson risk model with a constant tax, credit interest and debit interest rate; by Cheung and Landriault (2012) in the classical compound Poisson risk models with surplus-dependent premium and tax rate; by Wei et al. (2010) in the Markov-modulated risk models with constant tax rate; and by Kyprianou and Zhou (2009) in the Lévy risk models with surplus-dependent tax rate. One can find the earliest work for (2) and (3) in Albrecher and Hipp (2007) in the classical compound Poisson risk model with a constant tax rate. These results were then generalized ...

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On the expected discounted penalty function for risk process with tax

Cited by 14 publications

References 12 publications

The Tax Identity For Markov Additive Risk Processes

The Tax Identity For Markov Additive Risk Processes

Randomized Dividends in a Discrete Insurance Risk Model with Stochastic Premium Income

Optimal loss-carry-forward taxation for Lévy risk processes stopped at general draw-down time

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