1.
Thisistocertifythat
LudovicPAUL
hassuccessfullycompletedallcoursesandreceived
passinggradestoearnaMicroMastersprogram
certificatein
Finance
aprogramofferedbyMITx,incollaborationwithedX.
LeonidKogan
NipponTelegraph&TelephoneProfessorofManagement
MITSloanSchoolofManagement
JiangWang
MizuhoFinancialGroupProfessor
MITSloanSchoolofManagement
JohnE.Core
NanyangTechnologicalUniversityProfessorofAccounting
MITSloanSchoolofManagement
PaulF.Mende
SeniorLecturer
MITSloanSchoolofManagement

2.
MICROMASTERS PROGRAM CERTIFICATE
IssuedJanuary2023
VALID CERTIFICATE ID
62ded0a9923741e18aae4a27389505ab
DeborahLucas
SloanDistinguishedProfessorofFinance
MITSloanSchoolofManagement
EgorMatveyev
SeniorLecturer
MITSloanSchoolofManagement
W.EricL.Grimson
InterimVicePresidentforOpenLearning
MassachusettsInstituteofTechnology

3.
Verified Certificate
IssuedJanuary24,2023
Valid Certificate ID
8bc3f52bb74c4e0f8105b445a614de91
Thisistocertifythat
LudovicPAUL
successfullycompletedandreceivedapassinggradein
15.455x:MathematicalMethodsforQuantitative
Finance
acourseofstudyofferedbyMITx,anonlinelearninginitiative
oftheMassachusettsInstituteofTechnology.
PaulF.Mende
SeniorLecturer
MITSloanSchoolofManagement
EgorMatveyev
SeniorLecturer
MITSloanSchoolofManagement
EricGrimson
InterimVicePresidentforOpenLearning
MassachusettsInstituteofTechnology
ChrisCapozzola
SeniorAssociateDeanforOpenLearning
ProfessorofHistory
MassachusettsInstituteofTechnology

4.
Verified Certificate
IssuedOctober1,2022
Valid Certificate ID
ddfa4b030b4b412ebc9f6630c68c98a4
Thisistocertifythat
LudovicPAUL
successfullycompletedandreceivedapassinggradein
15.435x:DerivativesMarkets:AdvancedModeling
andStrategies
acourseofstudyofferedbyMITx,anonlinelearninginitiative
oftheMassachusettsInstituteofTechnology.
DeborahLucas
SloanDistinguishedProfessorofFinance
MITSloanSchoolofManagement
EgorMatveyev
ExecutiveDirectorofMicromastersPrograminFinance
MITSloanSchoolofManagement
SanjaySarma
VicePresidentforOpenLearning
MassachusettsInstituteofTechnology

5.
Verified Certificate
IssuedJuly17,2022
Valid Certificate ID
f6a3b1d9dd4e4b208a75587d2416a32c
Thisistocertifythat
LudovicPAUL
successfullycompletedandreceivedapassinggradein
15.516x:FinancialAccounting
acourseofstudyofferedbyMITx,anonlinelearninginitiative
oftheMassachusettsInstituteofTechnology.
JohnE.Core
NanyangTechnologicalUniversityProfessorofAccounting
MITSloanSchoolofManagement
EgorMatveyev
ExecutiveDirectorofMicroMastersPrograminFinance
MassachusettsInstituteofTechnology
SanjaySarma
VicePresidentforOpenLearning
MassachusettsInstituteofTechnology

6.
Thisistocertifythat
LudovicPAUL
successfullycompletedandreceivedapassinggradein
15.415.1x:FoundationsofModernFinanceI
acourseofstudyofferedbyMITx,anonlinelearninginitiative
oftheMassachusettsInstituteofTechnology.
LeonidKogan
NipponTelegraph&TelephoneProfessorofManagement,MIT
SloanSchoolofManagement
MassachusettsInstituteofTechnology
JiangWang
MizuhoFinancialGroupProfessor,MITSloanSchoolof
Management
MassachusettsInstituteofTechnology
EgorMatveyev
SeniorLecturer,MITSloanSchoolofManagement
MassachusettsInstituteofTechnology
EricGrimson
InterimVicePresidentforOpenLearning
MassachusettsInstituteofTechnology
ChrisCapozzola
SeniorAssociateDeanforOpenLearning
ProfessorofHistory