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AdvancesinAppliedMathematicsA^êÆ?Ð,2021,10(12),4218-4226
PublishedOnlineDecember2021inHans.http://www.hanspub.org/journal/aam
https://doi.org/10.12677/aam.2021.1012448
EÜPoisson.‘»v7•`©ùüÑ
ooo···•••
U9>f&E…’EâÆ²L†+nX§U9
ÂvFϵ2021c1113F¶¹^Fϵ2021c129F¶uÙFϵ2021c1116F
Á‡
© ïÄEÜPoisson.‘»v7•`©ù¯K"8I´•Œz»ž•ƒc\Èò
y ©ùÚòyv7ƒ"Äk§©‰ÑŠ¼ê÷vÄ5Ÿ",§©íŠ¼ê÷
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'…c
EÜPoisson.§•`©ù¯K§v7¼ê§HJB•§
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-
©ÙÚ^:o·•.EÜPoisson.‘»v7•`©ùüÑ[J].A^êÆ?Ð,2021,10(12):4218-4226.
DOI:10.12677/aam.2021.1012448
o·•
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.2021.10124484221A^êÆ?Ð
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DOI:10.12677/aam.2021.10124484222A^êÆ?Ð
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DOI:10.12677/aam.2021.10124484223A^êÆ?Ð
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0 = cV
0
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x
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