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AdvancesinAppliedMathematics
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,2021,10(12),4218-4226
PublishedOnlineDecember2021inHans.http://www.hanspub.org/journal/aam
https://doi.org/10.12677/aam.2021.1012448
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OptimalDividend-PenaltyStrategyinthe
CompoundPoissonModel
JingweiLi
DepartementofEconomicsandManagement,TianjinElectronicInformationCollege,Tianjin
Received:Nov.13
th
,2021;accepted:Dec.9
th
,2021;published:Dec.16
th
,2021
Abstract
Thispaperconcersanoptimaldividend-penaltyproblemforthecompoundPoisson
model.Theobjectiveistomaximizethedifferenceoftheexpectedcumulativedis-
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DOI:10.12677/aam.2021.1012448
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countedpenaltypaymenttakenatthemomentofruinandadiscountedpenaltypay-
menttakenatthemomentofruin.Firstly,thispapergivesthebasicpropertiesof
thevaluefunction.Then,wederivetheHJBequationofthevaluefunction.Finally,
itisverifiedthatthevaluefunctionisthesolutionoftheHJBequation.
Keywords
CompoundPoissonMode,OptimalDividendProblem,Gerber-ShiuFunction,
HJBEquation
Copyright
c
2021byauthor(s)andHansPublishersInc.
This work is licensed undertheCreative Commons Attribution InternationalLicense(CCBY4.0).
http://creativecommons.org/licenses/by/4.0/
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DOI:10.12677/aam.2021.10124484222
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DOI:10.12677/aam.2021.10124484223
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DOI:10.12677/aam.2021.10124484224
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