Omega Model for a Jump-Diffusion Process with a Two-Step Premium Rate and a Threshold Dividend Strategy

Gao, Zhongqin; He, Jianjia; Zhang, Zhao; Wang, Bingbing

doi:10.1007/s11009-020-09844-4

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…In the Cramér-Lundberg model with randomized observation periods [3], the Gerber-Shiu function solves a certain boundary value problem and is found in closed form for claims with rational Laplace transform, again when the penalty function w(x, y) is independent of x. Various structural features have been investigated in this context, for example, additional perturbation and a constant dividend barrier with claim sizes of rational transform [108], with a two-step premium rate allowing business after ruin occurs [59], perturbation and a constant interest with a periodic barrier dividend strategy [182], claim amounts of phase type [32], and a constant interest when the penalty function is independent of x [159]. Other features investigated include an additional stochastic premium modeled by a compound Poisson process with multiple layers [131], a hybrid dividend strategy [47], a stochastic interest modeled by a drifted Brownian motion and a compound Poisson process [161], and stochastic volatility driven by an Ornstein-Uhlenbeck process [42].…”

Section: Boundary Value Problemsmentioning

confidence: 99%

The Gerber-Shiu discounted penalty function: A review from practical perspectives

He¹,

Kawai²,

Shimizu³

et al. 2022

Preprint

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The Gerber-Shiu function provides a unified framework for the evaluation of a variety of risk quantities. Ever since its establishment, it has attracted constantly increasing interests in actuarial science, whereas the conventional research has been focused on finding analytical or semi-analytical solutions, either of which is rarely available, except for limited classes of penalty functions on rather simple risk models. In contrast to its great generality, the Gerber-Shiu function does not seem sufficiently prevalent in practice, largely due to a variety of difficulties in numerical approximation and statistical inference. To enhance research activities on such implementation aspects, we provide a full review of existing formulations and underlying surplus processes, as well as an extensive survey of analytical, semi-analytical and asymptotic methods for the Gerber-Shiu function, which altogether shed fresh light on its numerical methods and statistical inference for further developments. On the basis of an exhaustive collection of 207 references, the present survey can serve as an insightful guidebook to model and method selection from practical perspectives as well.

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