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

Zhongqin Gao, Jingmin He (), Zhifeng Zhao and Bingbing Wang
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Zhongqin Gao: Tianjin University of Technology
Jingmin He: Tianjin University of Technology
Zhifeng Zhao: Sinosoft Company Limited
Bingbing Wang: Tianjin University of Technology

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 1, 233-258

Abstract: Abstract In this paper, a jump-diffusion Omega model with a two-step premium rate and a threshold dividend strategy is studied. For this model, the surplus process is a perturbation of a compound Poisson process by a Brownian motion. Firstly, using the strong Markov property, the integro-differential equations for the expected discounted dividend payments function, the Gerber-Shiu expected discounted penalty function and bankruptcy probability are derived. Secondly, for a constant bankruptcy rate function, the renewal equations satisfied by the expected discounted dividend payments function and the Gerber-Shiu expected discounted penalty function are obtained, respectively, and by iteration, their closed-form solutions are also given. Furthermore, the explicit solutions of the two kinds of functions are obtained when the individual claim size is subject to exponential distribution. Finally, a numerical example is presented to illustrate some properties of the Omega model.

Keywords: Omega model; Compound poisson; Diffusion; Threshold strategy; Dividend payments; Gerber-shiu function; Bankruptcy; Two-step premium rate; 62P20; 91B30 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-020-09844-4

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