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Optimal Dividend and Capital Injection Strategies in the Cramér-Lundberg Risk Model

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  • Yan Li
  • Guoxin Liu

Abstract

We discuss the optimal dividend and capital injection strategies in the Cramér-Lundberg risk model. The value function is defined by maximizing the discounted value of the dividend payment minus the penalized discounted capital injection until the time of ruin. It is shown that can be characterized by the Hamilton-Jacobi-Bellman equation. We find the optimal dividend barrier , the optimal upper capital injection barrier 0, and the optimal lower capital injection barrier . In the case of exponential claim size especially, we give an explicit procedure to obtain , , and the value function .

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  • Yan Li & Guoxin Liu, 2015. "Optimal Dividend and Capital Injection Strategies in the Cramér-Lundberg Risk Model," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-16, March.
    • Handle: RePEc:hin:jnlmpe:439537
    DOI: 10.1155/2015/439537
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    Cited by:

    1. Florin Avram & Dan Goreac & Juan Li & Xiaochi Wu, 2021. "Equity Cost Induced Dichotomy for Optimal Dividends with Capital Injections in the Cramér-Lundberg Model," Mathematics, MDPI, vol. 9(9), pages 1-27, April.

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