A financial market with interacting investors

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1、MathFinanEcon(2011)4:161182DOI10.1007/s11579-011-0039-0Afinancialmarketwithinteractinginvestors:doesanequilibriumexist?ChristophFrei·GonçalodosReisReceived:22October2010/Accepted:10February2011/Publishedonline:26February2011©Springer-Verlag2011AbstractWhiletradingonafinancialmarket,theagentswecons

2、idertaketheperfor-manceoftheirpeersintoaccount.Bymaximizingindividualutilitysubjecttoinvestmentconstraints,theagentsmayruineachotherevenunintentionallysothatnoequilibriumcanexist.However,whentheagentsarewillingtowaivelittleexpectedutility,anapproximatedequilibriumcanbeestablished.Thestudyoftheas

3、sociatedbackwardstochasticdifferen-tialequation(BSDE)revealsthemathematicalreasonfortheabsenceofanequilibrium.Presentinganillustrativecounterexample,weexplainwhysuchmultidimensionalquadraticBSDEsmaynothavesolutionsdespiteboundedterminalconditionsandincontrasttotheone-dimensionalcase.KeywordsRela

4、tiveperformance·Interactinginvestors·Approximatedequilibrium·MultidimensionalBSDE·QuadraticgeneratorMathematicSubjectClassification(2010)91B52·60H10·91G80JELClassificationG11·C621IntroductionAssumingyouhaveinvestedinafund,areyousatisfiedwiththefundmanagerifsheachievedaperformanceof4%inthelastyear?Y

5、oumaysaythattheanswerdependsmainlyontwofactors:theriskthemanagerhastakenandthedevelopmentofthemarketsinthelastyear.Inmathematicalfinance,thefrequentlyusedapproachofmaximizingexpectedutilityfromC.Frei(B)DepartmentofMathematicalandStatisticalSciences,UniversityofAlberta,Edmonton,ABT6G2G1,Canadae-ma

6、il:cfrei@ualberta.caG.dosReisInstitutfürMathematik,TechnischeUniversitätBerlin,Str.des17.Juni136,10623Berlin,Germanye-mail:dosreis@math.tu-berlin.de123162MathFinanEcon(2011)4:161182terminalwealthincorporatessimultaneouslytheperformanceandtheriskrelatedtoatrad-ingstrategy.However,therelativeperfo

7、rmancecomparedtoanindexorotherinvestorsistypicallynottakenintoaccount,althoughbenchmarkingmayevenbepartofhumannatureandisimportantforafundmanagerwhoneedstokeepthefundcompetitive.Thegoalofthisarticleistostudytheimpactsofinteg