Dividend and Capital Injection Optimization with Transaction Cost for Lévy Risk Processes

Wenyuan Wang (), Yuebao Wang (), Ping Chen () and Xueyuan Wu ()
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Wenyuan Wang: Xiamen University
Yuebao Wang: Soochow University
Ping Chen: The University of Melbourne
Xueyuan Wu: The University of Melbourne

Journal of Optimization Theory and Applications, 2022, vol. 194, issue 3, No 8, 924-965

Abstract: Abstract The optimal dividends problem has remained an active research field for decades. For an insurance company with reserve modelled by a spectrally negative Lévy process having finite first-order moment, we study the optimal impulse dividend and capital injection (IDCI) strategy for maximizing the expected accumulated discounted net dividend payment subtracted by the accumulated discounted cost of injecting capital. In this setting, the beneficiary of the dividends injects capital to ensure a non-negative risk process so that the insurer never goes bankrupt. The optimal IDCI strategy together with its value function is obtained. Besides, two numerical examples are provided to illustrate the features of the optimal strategies. The impacts of model parameters are also studied.

Keywords: Spectrally negative Lévy process; De Finetti’s optimal dividend problem; Stochastic control; Hamilton–Jacobi–Bellman inequality; 49K45; 49N25 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02057-4

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