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Optimal Parisian-Type Dividend Payments Penalized by the Number of Claims for the Classical and Perturbed Classical Risk Process

Czarna Irmina, Li Yanhong, Palmowski Zbigniew, Zhao Chunming

Probability and Mathematical Statistics

2020

Vol. 40, Fasc. 1

57--81

We consider the classical risk process (the case σ = 0) and the classical risk process perturbed by a Brownian motion (the case σ > 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.