一類g-概率的對稱性問題.pdf

1、山東大學碩士學位論文一類g概率的對稱性問題姓名：張靜申請學位級別：碩士專業(yè)：概率統計指導教師：陳增敬20070428山東大學碩士學位論文AbstractChoquet(1953)extendedtheprobabilitymeasurePin(0，1)toanonlinearprobabilitymeasureV(alsocalledthecapacity)andobtainthefollowingdefinitionG(f)ofnon

2、linearmathematicalexpectations(calledtheChoquetexpectation)：，U，∞c嬉)：=／【礦膳≥t)一1ldt／y任≥t)dtJ一∞J0Choquetexpectations，whichareusedtodealwithuncertainphenomena，havemanyapplicationsinstatistics，economics，financeandphysicsManyp

3、apersstudytheChoquetexpectationanditsapplications，flee，forexample，Anger(1977)，Dellacherie(1970)，Graf(1980)，SarinandWakker(1992)，Schmeidler(1989)，Wakker(2001)，WassermanandKadane(1990)andthereferencesthereinChoquetcapaciti

4、esarewidelyusedinrobustnessdecisiontheoryandgametheoryAkindofChoquetcapacities，whichiscalledsymmetric，coherentisreallyimporrantManycapacitiesthatariseinrobustnessaresymmetric，coherentcapacitiesorcanbetransformedintothesa

5、mebyasmooth，onetoonemapping[Buja(1986)，HuberandStrassen(1973)，WassermanandKadaae(1990)andFortiniandRuggeri(1994)]Manyotherpapersstudysymmetriccapacities，see，forexamples，Armstrong(1990)，Dempster(1967，1968)，AngerandLembcke

6、(1985)，Walley(1991)，Talagrand(1978)，WaseermanandKadane(1992)andSOonPengandPardoux(1990)introducedakindofequationcaUedbackwardstochasticdifferentialequation(BSDE)Peng(1997)introducedthenotionofgexpectationviabackwardstoch

7、asticdifferentialequationHeshowedthatundersuitablesquareintegrabilitya881nnptionsonthecoefficientgandtheterminalvaluef，thegexpectationofrandomvariablefpreservemanyofthebasicproperties(exceptlinearity)oftheconvenientmathe

8、matiealexpectationgexpectationhasbeenappliedinfinance，see，forexample，ChenandEpstein(2002)Chen(2005)studiedtherelationbetweengexpectationandChoquetexpectationandprovidedanecessaryandsufficientconditionInthispaper，wedefine