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On the Optimal Dividend Problem in the Dual Model with Surplus-Dependent Premiums

Author

Listed:
  • Ewa Marciniak

    (AGH University of Science and Technology)

  • Zbigniew Palmowski

    (Wrocław University of Science and Technology)

Abstract

This paper concerns the dual risk model, dual to the risk model for insurance applications, where premiums are surplus-dependent. In such a model, premiums are regarded as costs and claims refer to profits. We calculate the mean of the cumulative discounted dividends paid until the time of ruin, if the barrier strategy is applied. We formulate the associated Hamilton–Jacobi–Bellman equation and identify sufficient conditions for a barrier strategy to be optimal. Numerical examples are provided.

Suggested Citation

  • Ewa Marciniak & Zbigniew Palmowski, 2018. "On the Optimal Dividend Problem in the Dual Model with Surplus-Dependent Premiums," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 533-552, November.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:2:d:10.1007_s10957-016-1050-7
    DOI: 10.1007/s10957-016-1050-7
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    References listed on IDEAS

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    1. Gerber, Hans U. & Smith, Nathaniel, 2008. "Optimal dividends with incomplete information in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 227-233, October.
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    7. Ewa Marciniak & Zbigniew Palmowski, 2016. "On the Optimal Dividend Problem for Insurance Risk Models with Surplus-Dependent Premiums," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 723-742, February.
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    11. F. Avram & Z. Palmowski & M. R. Pistorius, 2011. "On Gerber-Shiu functions and optimal dividend distribution for a L\'{e}vy risk process in the presence of a penalty function," Papers 1110.4965, arXiv.org, revised Jun 2015.
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    Cited by:

    1. Osatakul, Dhiti & Li, Shuanming & Wu, Xueyuan, 2023. "Discrete-time risk models with surplus-dependent premium corrections," Applied Mathematics and Computation, Elsevier, vol. 437(C).

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