The Annals of Applied Probability应用概率年报

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1、TheAnnalsofAppliedProbability2015,Vol.25,No.6,3251–3294DOI:10.1214/14-AAP1073cInstituteofMathematicalStatistics,2015WEAKREFLECTIONPRINCIPLEFORLEVYPROCESSES´ByErhanBayraktar1andSergeyNadtochiyUniversityofMichiganInthispaper,wedevelopanewmathematicaltechniquewhichallowsustoexpressthejointdist

2、ributionofaMarkovprocessanditsrunningmaximum(orminimum)throughthemarginaldistri-butionoftheprocessitself.ThistechniqueisanextensionoftheclassicalreflectionprincipleforBrownianmotion,anditisobtainedbyweakeningtheassumptionsofsymmetryrequiredfortheclassicalreflectionprincipletowork.Wecallthisme

3、thodaweakreflectionprincipleandshowthatitprovidessolutionstomanyproblemsforwhichtheclassicalreflectionprincipleistypicallyused.Inaddition,unliketheclassicalreflectionprinciple,thenewmethodworksforamuchlargerclassofstochasticprocesseswhich,inparticular,donotpossessanystrongsymmetries.Here,werev

4、iewtheexistingresultswhichestablishtheweakreflectionprincipleforalargeclassoftime-homogeneousdiffusionsonareallineandthenproceedtoextendthismethodtotheL´evyprocesseswithone-sidedjumps(subjecttosomeadmissibilityconditions).Finally,wedemonstratetheapplicationsoftheweakreflectionprincipleinfinanci

5、almathematics,computationalmethodsandinverseproblems.1.Introduction.1.1.Classicalreflectionprincipleanditsapplications.WestartwithabriefreviewoftheclassicalreflectionprincipleforBrownianmotion.DenotebyBxtheBrownianmotiononarealline,startedformx.GivenarbitrarylevelsU>0andK

6、ntdistributionofBt=Bt0anditsrunningmaximumMt=supu∈[0,t]Buasfollows:arXiv:1308.2250v4[math.PR]26Oct2015P(Bt≤K,Mt>U)=P(B≤K,T

7、onprinciple,L´evyprocesses,statichedging,barrierop-tions.ThisisanelectronicreprintoftheoriginalarticlepublishedbytheInstituteofMathematicalStatisticsinTheAnnalsofAppliedProbability,2015,Vol.25,No.6,3251–3294.Thisreprintdiffersfromtheoriginalinpaginationan