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On the closed-form expected NPVs of double barrier strategies for regular diffusions

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  • Chongrui Zhu

Abstract

The core of the research is to provide the explicit expression for the expected net present values (NPVs) of double barrier strategies for regular diffusions on the real line without solving differential equations. Under the so-called bail-out setting, the value of the expected NPVs of an insurance company varies according to the choice of a pair of policies, which consist of dividend payments paid out and capital injections received. In the case of the double barrier strategy, the expected NPVs are expressible with the help of certain types of functions allowing explicit expression in some cases, which is called the bivariate $q$-scale function in the article. This is accomplished by making use of a perturbation technique in \cite{czarna2014dividend}, which could lead to the linear equation system. In addition, a condition ensuring the existence of an optimal (upper) barrier level is presented. In the end, examples fitting the condition for selecting the optimal barrier are given.

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  • Chongrui Zhu, 2022. "On the closed-form expected NPVs of double barrier strategies for regular diffusions," Papers 2206.08922, arXiv.org, revised Dec 2022.
    • Handle: RePEc:arx:papers:2206.08922
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    1. Benjamin Avanzi & Jos'e-Luis P'erez & Bernard Wong & Kazutoshi Yamazaki, 2016. "On optimal joint reflective and refractive dividend strategies in spectrally positive L\'evy models," Papers 1607.01902, arXiv.org, revised Nov 2016.
    2. Noba, Kei & Pérez, José-Luis & Yamazaki, Kazutoshi & Yano, Kouji, 2018. "On optimal periodic dividend strategies for Lévy risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 29-44.
    3. Loeffen, Ronnie L. & Renaud, Jean-François, 2010. "De Finetti's optimal dividends problem with an affine penalty function at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 98-108, February.
    4. Kei Noba & Jos'e-Luis P'erez & Kazutoshi Yamazaki & Kouji Yano, 2017. "On optimal periodic dividend strategies for L\'evy risk processes," Papers 1708.01678, arXiv.org, revised Feb 2018.
    5. Bayraktar, Erhan & Kyprianou, Andreas E. & Yamazaki, Kazutoshi, 2014. "Optimal dividends in the dual model under transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 133-143.
    6. M. R. Pistorius, 2004. "On Exit and Ergodicity of the Spectrally One-Sided Lévy Process Reflected at Its Infimum," Journal of Theoretical Probability, Springer, vol. 17(1), pages 183-220, January.
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