Pricing in an equilibrium based model for a large investor

《Pricing in an equilibrium based model for a large investor》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、MathFinanEcon(2011)4:287297DOI10.1007/s11579-011-0041-6PricinginanequilibriumbasedmodelforalargeinvestorDavidGermanReceived:16February2011/Accepted:9March2011/Publishedonline:26March2011©Springer-Verlag2011AbstractWestudyafinancialmodelwithanon-trivialpriceimpacteffect.Inthismodelweconsiderthe

2、interactionofalargeinvestortradinginanilliquidsecurity,andamarketmakerwhoisquotingpricesforthissecurity.Weassumethatthemarketmakerquotesthepricessuchthatbytakingtheothersideoftheinvestorsdemand,themarketmakerwillarriveatmaturitywiththemaximalexpectedutilityoftheterminalwealth.Withinthismodelw

3、eprovideanexplicitrecursivepricingformulaforanexponentialutilityfunction,aswellasanasymptoticexpansionforthepriceforasmallsimpledemand.KeywordsLargeinvestor·Liquidity·Utilityoptimization·EquilibriumJELClassificationC60·G121IntroductionThestudyofcontingentclaimvaluationproblemaccountsforalargen

4、umberofpapersinFinance,EconomicsandMathematicalFinanceinparticular.Thisquestionwasandcur-rentlyisstudiedbymanyauthorsinvariousmodelsunderdifferentassumptions.Acom-monassumptionmadebymanyauthorsisthebasiceconomicassumption(imposedeitherimplicitlyorexplicitly)thataneconomicagentcantradeanysecur

5、ityinthedesiredquantityatthesameprice.Theconsequenceofthisassumptionisthattheeconomicagentsactionsdonotaffectthetradedsecuritysprice,andthatthereisneverashortageofanysecurityinanyquantity.Onewaytorelaxthisassumptionistoconsideramodelwhereagentsactionsmoveprices.Wewillachievethatbyintroducingt

6、henotionofliquidityintothemodel.Liquidityisacomplexconceptstandingfortheeaseoftradingofasecurity.(Il)liquiditycanhaveD.German(B)DepartmentofMathematicalSciences,ClaremontMcKennaCollege,850ColumbiaAve.,Claremont,CA91711,USAe-mail:dgerman@cmc.edu123288MathFinanEcon(2011)4:287297differentsources

7、,suchasinventoryriskStoll[15],transactioncostsCvitani´candKaratzas[4],uncertainholdinghorizonsHuang[13],asymmetryofinformationGârleanuandPedersen[9],demandpressureGârleanuetal.[10],searchfrictionDuffieetal.[6],stochasticsupplycurveÇetinetal.[3