一类稀疏模型的期望折现分红函数

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1、-•H“‰ŒÆa¬ÆØ©AbstractInthedualriskmodel,gainisthemainwayforacompanythatspecializesininventionsanddiscoveries.Therefore,thedividend-paymentstrategyofdualriskmodelhasbecomeoneofthecurrenttopics.Wealwaysassumethatexpenseisalinearfunctioninthedualriskmodel.Andtheexpensearrivingnumberprocess

2、isindependentwiththegainarrivingnumberprocess.Actually,itisnotenoughtofullydescribethesituation.Sothemoredependentmodelisstudied.Weintroducebarrierstrategyandthresholdstrategytothemodelonthebasisofthedualriskmodelandgeneralizetomoregeneralcasewhichexpensenumberprocessisnolongeraconstan

3、tbutarandomvariable.Weassumetheexpensearrivingnumberpro-cessN(t)isaPoissonprocesswithparameterλ>0M˙eantime,thegainnumberarrivingprocessNp(t)isathinningprocessoftheexpensearrivingnumberprocess.Weobtaintheintegraldifferentialequationoftheexpecteddiscounteddividendfunctionunderdiffer-entdiv

4、idendstrategy,andwealsogivestheintegraldifferentialequationoftheexpecteddiscountedpenaltyfunctionunderbarriersdividendstrategy.Finnally,weobtainsolutiontotheintegraldifferentialequationwhenexpenseandprofitsizesareexponentiallydis-tributed.Thispaperisdividedintofourchapter:Inchapterone,wei

5、ntroducethecurrentresearchsituationofdualriskmodel,randompremiumanddividendproblem.WealsointroducethedependentriskmodelUt=u−XNti=1Xi+pNXti=1Yi+σBtInchaptertwo,firstly,wederiveanintegralequationfortheexpecteddiscounteddividendpaymentswiththebarrierdividendintothemodel.σ22V(2)(u;b)−(λ+δ)V

6、(u;b)+(1−p)λZV(u;b)dF(x)u---+pλZγb(u+y−b)dG(y)=0,0∞0whenexpenseandprofitsizesareexponentiallydistributed,V(u;b)=Σ4i=1CieξInchapterthree,atfirst,wederiveanintegralequationfortheexpecteddiscountediii万方数据---•H“‰ŒÆa¬ÆØ©dividenduntilruinunderthethresholddividendstrategy.0≤u

7、)(u;b)−(λ+δ)V(u;b)+(1−p)λZV(u−x;b)dF(x)σ2u20+pλZ0ZV(u−x+y;b)dF(x)dG(y)=0,.∞u+y0u≥b,V(u;b)satisfiedσ22V(2)(u;b)−cV0(u;b)−(λ+δ)V(u;b)+(1−p)λZV(u−x;b)dF(x)u0+pλZ0ZV(u−x+y;b)dF(x)dG(y)+c=0.∞u+y0Inchapterfour,wederiveanintegralequationfortheexpectedpenaltydividendunderthebarrierdividendstr