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The Ornstein-Uhlenbeck-type model with a hybrid dividend strategy. (English) Zbl 1397.91297

Summary: 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.

MSC:

91B30 Risk theory, insurance (MSC2010)
60J60 Diffusion processes
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