[PDF] MATHÉMATIQUES FINANCIÈRES notamment le livre de ré

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)Capital )Capital )Capital )Capital ??????? ???? ? ????UM ) =???UM ??????? ???? ? ????UM ) =???UM ??????? ???? ? ????UM ) =???UM ??????? ???? ? ????UM ) =???UM ??? ????? ?????? ?VF= (?+t??? )nVA??VA=?(?+t??? )nVF= (?+t??? )nVF

VF=k=nX

??? ????? ?????? ?VF= (?+t??? )nVA??VA=?(?+t??? )nVF= (?+t??? )nVF

VF=k=nX

??? ????? ?????? ?VF= (?+t??? )nVA??VA=?(?+t??? )nVF= (?+t??? )nVF

VF=k=nX

VF=Vk=nX

k=?(?+t??? )nk=V(?+t??? )n?t

VA=k=nX

k=?X k(?+t???

VF=Vk=nX

k=?(?+t??? )nk=V(?+t??? )n?t

VA=k=nX

k=?X k(?+t???

VA=Vk=nX

k=??(?+t??? )k=Vk=nX k=?(?+t??? )k=V?(?+t??? )nt

VA=Vk=nX

k=??(?+t??? )k=Vk=nX k=?(?+t??? )k=V?(?+t??? )nt ??????? ?? ???? ??????? ???? ? ???? ?????UM? ???? ??? ?? P P P D R t=Dt+PtPt?P R t=PtPt?P t?=)Pt= (?+Rt)Pt? P t?=Pt?+Rt R t=PtPt?P t?=)Pt= (?+Rt)Pt? P t?=Pt?+Rt P t?=???UM P t=???UM D t=?UM R R R

VAR(aX+bY) =a?VAR(X) +b?VAR(Y) +?abCOV(X;Y)

COV(X;Y) =ESP(XESP(X))(YESP(Y)) =Xp

i(XiX)(YiY) =?n

X(XiX)(YiY)

CC

AB=COV(RA;RB)

RARB ?P=X?A?RA+X?b?RB+?XAXBRARBCCAB CC ?? %???%??A??? ??%??A??? D t+?=?? ??Dt+?=???? D t+?=?? ??Dt+?=???? P ?=k=nX k=?D ??????? ?P ?=+1X k=?D P ?=k=nX k=?D ??????? ?P ?=+1X k=?D P ?=k=nX k=?D ??????? ?P ?=+1X k=?D ?=k=nX k=?(?+g)k?D?(?+r)k+Pn(?+r)n=D??+rk=nX k=? ?+g?+r k? +Pn(?+r)n P ?=D??+r2

4??+g?+r

n??+g?+r3 5 ?=k=nX k=?(?+g)k?D?(?+r)k+Pn(?+r)n=D??+rk=nX k=? ?+g?+r k? +Pn(?+r)n P ?=D??+r2

4??+g?+r

n??+g?+r3 5 P ?=D?(?+r) ??+g?+r ??+g?+r n +Pn(?+r)n P ?=D?rg ??+g?+r n ?????? ??????? ?? ???gP=k=nX k=?x kAkk=nX k=?x k=? P min8 k=?xk=??? P max8 ?? ?????? ?? ?????? ???P=P??Pk=n P min8 k=?xk=??? P max8 ?? ?????? ?? ?????? ???P=P??Pk=n

P=k=nX

k=?x kAk R p=k=nX k=?x

Cov(Ak;Ak0)6=?? ?? ? ?

?P=k=nX k=?x ?k?Ak+?X ?kCCAXT=x?x?xn 0 B

BB@Cov(A?;A?)Cov(A?;A?)Cov(A?;An)

Cov(A?;A?)Cov(A?;A?)Cov(A?;An)

Cov(An;A?)Cov(An;A?)Cov(An;An)1

C CCA 0 B BB@ ?A ?Cov(A?;A?)Cov(A?;An)

Cov(A?;A?)?A

?Cov(A?;An)

Cov(An;A?)Cov(An;A?)?A

n1 C

L=k=nX

k=?k 0=nX k 0=?x kxk0Cov(Ak;Ak0) |{z} k=?x kRAkRP |{z} k=?x k? |{z} @L@xk=?k=?;;n @L@ ?=? ??@L@

L=k=nX

k=?k 0=nX k 0=?x kxk0Cov(Ak;Ak0) |{z} k=?x kRAkRP |{z} k=?x k? |{z} @L@xk=?k=?;;n @L@ ?=? ??@L@ 8 >>>>>>>>>>>>>>>>>>:?xkCov(A?;Ak)|{z} ?x?Var(A?) ++ ++?xnCov(A?;An) +?RA?+?=? ??? ?xkVar(Ak)|{z} ?x?Cov(Ak;A?) ++ ++?xnCov(Ak;An) +?RAk+?=? ??? ?xkCov(An;Ak)|{z} ?x?Cov(An;A?) ++ ++?xnVar(An) +?RAn+?=? x ?RA?++xkRAk++xnRAnRP=? x

AX=B???? ?

A=0 B ?Cov(A?;A?)?Var(A?)?Cov(A?;An)RA?? ?Cov(An;A?)?Cov(An;A?)?Var(An)RAn? R

A?RA?RAn? ?

? ?? ? ?1 C

AX=B???? ?

A=0 B ?Cov(A?;A?)?Var(A?)?Cov(A?;An)RA?? ?Cov(An;A?)?Cov(An;A?)?Var(An)RAn? R

A?RA?RAn? ?

? ?? ? ?1 C X=0 B

BBBBBBBBBBB@x

x x k??? x n ?1 C

CCCCCCCCCCCAB=0

B

BBBBBBBBBBB@?

R P?1 C

CCCCCCCCCCCA

L= k=nX

k=?x kRAkk=nX k=?k 0=nX k 0=?x kxk0Cov(Ak;Ak0) |{z} k=?x k) |{z} AX=B A=0 B

BBBB@?Var(A?)?Cov(A?;A?)?Cov(A?;An)?

?Cov(A?;A?)?Var(A?)?Cov(A?;An)? ?Cov(An;A?)?Cov(An;A?)?Var(An)? ? ?? ?1 C X=0 B

BBBBBBBBB@x

x x k??? x n 1 C

CCCCCCCCCAB=0

B

BBBBBBBBB@RA?RA????

RAk???

RAn?1 C

CCCCCCCCCA

??? ??????? ????P??P????Pn? k=?Pknk? x k=Pknk=cap? R kt=k+kRmt+"ktR ?? ???????t? R kt=k+kRmt+"ktR ?? ???????t? R kt=k+kRmt+"ktR ?? ???????t? R kt=k+kRmt+"ktR ?? ???????t? R kt=k+kRmt+"ktR ?? ???????t? R kt=k+kRmt+"ktR ?? ???????t? k=km ?m=Cov(Rk;RmVar(Rm) k=km ?m=Cov(Rk;RmVar(Rm) k=km ?m=Cov(Rk;RmVar(Rm) k=E(Rkt)kE(Rmt) k=E(Rkt)kE(Rmt) k=E(Rkt)kE(Rmt) ?P=?P?m+?"P ???? ?P=?N P kk???"P=?N ?P k"k=?N R kt=k+?kf?k+?kf?k++jkfjk R acheteurcall=???(?;SK)p R vendeurcall=???(?;KS) +p=???(?;SK) +p R acheteurput=???(?;KS)p R vendeurput=???(?;SK) +p=???(?;KS) +p d=?+r??u=?+r+ =fuuu;uud;udu;udd;duu;dud;ddu;dddg Squotesdbs_dbs47.pdfusesText_47

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