Optimal dividend strategies in a dual model with capital injections

Dai, Hongshuai; Liu, Zaiming; Luan, Nana

doi:10.1007/s00186-010-0312-7

Cited by 24 publications

(24 citation statements)

References 11 publications

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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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“…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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“…Owing to its practical importance, much research on the optimal dividend problem has been carried out for various surplus processes. For recent works, see Gerber and Shiu (2006), Fang and Wu (2009), Loeffen (2009a, b), Bai and Paulsen (2010), Wong and Zhao (2011), Yao et al (2011), Dai et al (2010), Dai and Liu (2011), Bai et al (2012), Zhu (2014) and Tan et al (2014). Although research on optimal dividend strategies in the Cramér-Lundberg risk models and the diffusion models has reached a state of maturity, very little work considered optimal dividend strategies under a penalty for ruin, specially in dependent increment models such as the delayed claim models.…”

Section: Introductionmentioning

confidence: 99%

Optimal dividend strategies in a delayed claim risk model with dividends discounted by stochastic interest rates

Tan

et al. 2015

Math Meth Oper Res

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We consider a discrete-time risk model with delayed claims and a dividend payment strategy. It is assumed that every main claim will induce a by-claim which may be delayed for one time period with a certain probability. In the evaluation of the expected present value of dividends, the interest rates are assumed to follow a Markov chain with finite state space. Dividends are paid to the shareholders according to an admissible strategy. The company controls the amount of dividends in order to maximize the cumulative expected discounted dividends prior to ruin minus the expected discounted penalty value at ruin. We obtain some properties of the optimal dividend-payment strategy, and offer high efficiency algorithms for obtaining the optimal strategy, the optimal value function and the expectation of time of ruin under the optimal strategy. Our method is mainly to transform the value function. Numerical examples are presented to illustrate the transformation method and the impact of the penalty for ruin on the optimal strategy, the corresponding expected present value of dividends and the expectation of time of ruin.

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Optimal dividend strategies in a dual model with capital injections

Cited by 24 publications

References 11 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

Duality in ruin problems for ordered risk models

Optimal dividend strategies in a delayed claim risk model with dividends discounted by stochastic interest rates

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