Abstract
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.
Highlights
The dividend problem has gained a lot of attention in the actuarial literature
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
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
Summary
The dividend problem has gained a lot of attention in the actuarial literature. 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. Optimal dividend in an Ornstein-Uhlenbeck-type model with credit and debit interest was considered in Cai et al [9]. For a class of compound Poisson process perturbed by diffusion with a threshold dividend strategy, the expected discounted penalty function has been studied by Wan [7]. The perturbed Sparre Andersen and compound Poisson risk models with multilayer dividend strategy have been studied by Yang and Zhang [11, 12]. Motivated by the above work, in this paper, we consider a hybrid dividend strategy which combined a barrier strategy with a threshold strategy in an Ornstein-Uhlenbeck-type model.
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