A perturbed risk process compounded by a geometric Brownian motion with a dividend barrier strategy

Gao, Heli; Yin, Chuancun

doi:10.1016/j.amc.2008.08.029

Cited by 5 publications

(3 citation statements)

References 18 publications

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“…Furthermore, they obtained the maximum severity of ruin and the distribution of the amount of dividends under a constant dividend barrier. Gao and Yin [6] investigated a perturbed risk process (in which the inter-occurrence times are generalized Erlang(n)-distributed) compounded by a geometric Brownian motion. Compared with these papers, we use a different method to study the ruin problem of Sparre Anderson risk model.…”

Section: Introductionmentioning

confidence: 99%

Ruin probability in Sparre Andersen risk model with claim inter-arrival times distributed as Erlang

2015

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This article deals with the ruin probability in a Sparre Andersen risk process with the inter-claim times being Erlang distributed in the framework of piecewise deterministic Markov process (PDMP). We construct an exponential martingale by virtue of the extended generator of the PDMP to change the measure. Some results are derived for the ruin probabilities, such as the general expressions for ruin probability, Lundberg bounds, Cramér-Lundberg approximations, and finite-horizon ruin probability.

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Section: Introductionmentioning

confidence: 99%

Ruin probability in Sparre Andersen risk model with claim inter-arrival times distributed as Erlang

2015

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“…Some recent papers extended the model to renewal risk models with stochastic return, see e.g. Gao and Yin (2008) and Li (2012).…”

Section: Introductionmentioning

confidence: 99%

An extension of Paulsen–Gjessing’s risk model with stochastic return on investments

Yin

Wen

2013

Insurance: Mathematics and Economics

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We consider in this paper a general two-sided jump-diffusion risk model that allows for risky investments as well as for correlation between the two Brownian motions driving insurance risk and investment return. We first introduce the model and then find the integro-differential equations satisfied by the Gerber-Shiu functions as well as the expected discounted penalty functions at ruin caused by a claim or by oscillation; We also study the dividend problem for the threshold and barrier strategies, the moments and moment-generating function of the total discounted dividends until ruin are discussed. Some examples are given for special cases.

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“…Dividend strategies for insurance risk model were first proposed by de Finetti [1], who considered a discrete time random walk with step size ±1 and found that the optimal dividend strategy must be a barrier strategy. From then on, the problem of optimal dividend strategy has been studied in continuous time, for example, Asmussen and Taksar [2], Albrecher et al [3], Gao and Yin [4], Gerber and Shiu [5,6], Wan [7] and so on. The optimal dividend problem in a compound Poisson model was studied by Gerber and Shiu [8].…”

Section: Introductionmentioning

confidence: 99%

The Ornstein-Uhlenbeck-Type Model with a Hybrid Dividend Strategy

Zhu

Yin

2013

Journal of Applied Mathematics

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We consider the Ornstein-Uhlenbeck-type model. We first introduce the model and then find the ordinary differential equations and boundary conditions satisfied by the dividend functions; closed-form solutions for the dividend value functions are given. We also study the distribution of the time value of ruin. Furthermore, the moments and moment-generating functions of total discounted dividends until ruin are discussed.

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A perturbed risk process compounded by a geometric Brownian motion with a dividend barrier strategy

Cited by 5 publications

References 18 publications

Ruin probability in Sparre Andersen risk model with claim inter-arrival times distributed as Erlang

Ruin probability in Sparre Andersen risk model with claim inter-arrival times distributed as Erlang

An extension of Paulsen–Gjessing’s risk model with stochastic return on investments

The Ornstein-Uhlenbeck-Type Model with a Hybrid Dividend Strategy

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