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

Chongrui Zhu
Jun 2022
摘要
The core of the research is to provide the explicit expression for theexpected net present values (NPVs) of double barrier strategies for regulardiffusions on the real line without solving differential equations. Under theso-called bail-out setting, the value of the expected NPVs of an insurancecompany varies according to the choice of a pair of policies, which consist ofdividend payments paid out and capital injections received. In the case of thedouble barrier strategy, the expected NPVs are expressible with the help ofcertain types of functions allowing explicit expression in some cases, which iscalled the bivariate $q$-scale function in the article. This is accomplished bymaking use of a perturbation technique in \cite{czarna2014dividend}, whichcould lead to the linear equation system. In addition, a condition ensuring theexistence 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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