复合二项对偶模型的最优分红策略

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1、AbstractThispaperdiscusstheproblemoftheoptimaldividend-paymentsincom-poundbinomialdualmodel.WedescribeafullydiscretedualmodelandobtaintheoptimalvaluefunctionbyanalysingtheHJBequation.WeusingBellmanre-cursivealgorithmtocalculatetheoptimalvaluefunction

2、andtheoptimaldividendstrategy.Thenweprovetwofunctionsapproachoftheoptimalvaluefunction.Inaddition,weusenumericalexamplestoillustrateauthenticityofthealgorithm.Inordertobemorerealistic,thenweconsidertheoptimaldividendproblemwithcapitalinjectionswithpr

3、oportionaltransactioncostsbasedonthediscretemodel,wherethedividenddiscountrateisrandomvariables.Wedescribethediv-idendsandcapitalinjectionsarerespectivelytwo{Ft}adaptedrandomsequences.Bytransformingthevaluefunctionintothecorrespondingimagefunction,we

4、an-alyzeanddiscussthepropertiesofimagefunctionandthecalculationmethodforoptimaldividendstrategy.Accordingtothenumericalsolutions,wealsondthatwhentransactioncostslessthanacertainproportionfortheinjectionsthevalueoftheoptimalstrategyisgreaterthantheca

5、sewithoutinjection.Keywords:Compoundbinomialdualmodel;HJBequation;Optimaldividendstrategy;Stochasticinterestrate;Capitalinjection;II目录第一章绪论........................................................(1)1.1分红问题的现状..........................................

6、.......(1)1.2文章的思路.....................................................(2)第二章复合二项对偶模型及假设......................................(4)2.1复合二项对偶模型..............................................(4)2.2基本假设......................................................

7、..(4)第三章最优分红策略和最优值函数...................................(6)3.1HJB方程和最优值函数..........................................(6)3.2分红策略的一些性质............................................(9)3.3最优值函数的无限逼近.........................................(10)3.4数值计算.........

8、..............................................(13)第四章随机利率下考虑注资的最优分红策略.........................(18)4.1模型与基本假设................................................(18)4.1红利有上界限制下的最优策略和最优值函数....................(19)4.2最优像函数的无限逼近...............................