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Contents of PMS, Vol. 40, Fasc. 1,
pages 57 - 81
DOI: 10.37190/0208-4147.40.1.4
Published online 20.3.2020
 

Optimal Parisian-type dividend payments penalized by the number of claims for the classical and perturbed classical risk process

Irmina Czarna
Zbigniew Palmowski
Yanhong Li
Chunming Zhao

Abstract: We consider the classical risk process (the case \(\sigma=0\)) and the classical risk process perturbed by a Brownian motion (the case \(\sigma>0\)). We analyze the expected NPV describing the mean of the cumulative discounted dividend payments paid up to the Parisian or classical ruin time and further penalized by the number of claims that appeared up to that time. We identify this function for a constant barrier strategy and we find sufficient conditions for this strategy to be optimal. We also analyze a numerical example of exponential claim sizes.

2010 AMS Mathematics Subject Classification: Primary 60J99; Secondary 93E20, 60G51.

Keywords and phrases: classical risk model, diffusion process, number of claims, Parisian ruin, dividend.

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