Paramëtres de Couverture et Risk Management - Maths-Fi

Sdxo Ghph|
Jdîo Ulerxohw
Sdudpëwuhv gh Frxyhuwxuh
hw Ulvn Pdqdjhphqw
Ohv pdufkìv g*rswlrqv ruhqw gh qrpeuhxvhv rssruwxqlwìv gh vsìfxodwlrq/ gh frxyhuwxuh hw
g*duelwudjh1 Dq g*dpìolruhu od uhqwdelolwì hw gh phvxuhu ohv ulvtxhv sulv/ lo hvw lqglvshqvdeoh gh
glvsrvhu g*rxwlov gh jhvwlrq txl shuphwwhqw xqh txdqwlfdwlrq gh od gìshqgdqfh gx frxuv g*xqh
rswlrq dx vrxv0mdfhqw1 Ohv lqglfdwhxuv whov txh oh ghowd/ oh jdppd/ oh yhjd/ oh wkíwd/ hw oh ukr
phvxuhqw o*hhw/ vxu od ydohxu g*xqh rswlrq +rx g*xq sruwhihxlooh g*rswlrqv,/ g*xqh yduldwlrq gh
fkdfxqh ghv yduldeohv gìwhuplqdqw fhwwh ydohxu/ wrxwhv fkrvhv ìjdohv sdu dloohxuv1
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Oh frh!flhqw ghowd
Oh ghowd g*xqh rswlrq/ qrwì / hvw od vhqvlelolwì gx sul{ gh fhwwh rswlrq ã o*dfwli vrxv0mdfhqw1
Lo shxw íwuh h{sulpì hq prqwdqw rx hq srxufhqwdjh1 Dlqvl/ xq ghowd gh 83( vljqlh txh od ydohxu
gh o*rswlrq hvw ghx{ irlv prlqv vhqvleoh txh o*dfwli vrxv0mdfhqw dx{ yduldwlrqv gx pdufkì = ã xqh
xfwxdwlrq g*xq iudqf gx frxuv gh o*dfwlrq vxu xq lqwhuydooh gh whpsv uìgxlw ghyud fruuhvsrqguh xqh
xfwxdwlrq gh 318 iudqf gh o*rswlrq1 Oh ghowd v*h{sulph pdwkìpdwltxhphqw frpph ìwdqw od gìulyìh
suhplëuh gx sul{ gh o*rswlrq sdu udssruw dx sul{ gx vrxv0mdfhqw1
Od qrwlrq gh ghowd v*ìwhqg ã xq sruwhihxlooh g*rswlrqv sruwdqw vxu oh píph vrxv0mdfhqw1 Oh ghowd
g*xq sruwhihxlooh hvw doruv od vrpph ghv ghowdv gh wrxwhv ohv srvlwlrqv gx sruwhihxlooh1
Fhw lqglfdwhxu uhyíw xqh lpsruwdqfh fdslwdoh srxu xq wudghu txl fkhufkh ã lqvhqvlelolvhu vrq
sruwhihxlooh ã wrxw prxyhphqw gx vrxv0mdfhqw hw grqf ã frqvwuxluh xq sruwhihxlooh vdqv ulvtxh1 Rq
sduoh doruv gh frxyhuwxuh hq ghowd0qhxwuh rx gh ghowd khgjlqj1 Sudwltxhphqw/ fhod frqvlvwh sdu
h{hpsoh ã yhqguh xqh rswlrq hw ã dfkhwhu dfwliv vrxv0mdfhqwv1 Dlqvl/ xqh ìyroxwlrq gìidyrudeoh
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gh od ydohxu gh o*rswlrq hvw frpshqvìh sdu o*ìyroxwlrq idyrudeoh gh o*dfwli vrxv0mdfhqw1 Wrxwhirlv/ oh
ghowd ydulh dyhf oh whpsv hw od ydohxu gx vrxv0mdfhqw1 Fhod vljqlh txh oh qrpeuh g*dfwliv ã srvvìghu
srxu lppxqlvhu vrq sruwhihxlooh ydulh frqvwdpphqw hw tx*xq wudghu grlw uììtxloleuhu vrq sruwhihxlooh
hq frqwlqx +f*hvw0ã0gluh dfkhwhu rx yhqguh xqh fhuwdlqh txdqwlwì g*dfwliv gh pdqlëuh ã dqqxohu/ ã
qrxyhdx/ oh ghowd gx sruwhihxlooh,1
Gdqv oh fdv gh pdufkìv oltxlghv hw ã idleohv frþwv gh wudqvdfwlrq/ xqh frxyhuwxuh hq ghowd0
qhxwuh shxw íwuh plvh hq rhxyuh1 Vxu ghv pdufkìv prlqv oltxlghv rx ã frþwv gh wudqvdfwlrq ìohyìv/
lo hvw vrxyhqw wuëv frxwhx{ gh uììtxloleuhu vrq sruwhihxlooh/ hw od frxyhuwxuh hvw doruv uhyxh prlqv
iuìtxhpphqw1 Gdqv fh ghuqlhu fdv/ oh ghowd qh shxw vx!uh ã phvxuhu od yduldwlrq g*xq sruwhihxlooh
gxh ã ghv prxyhphqwv soxv odujhv gx vrxv0mdfhqw1 Rq suhqg doruv hq frpswh xq lqglfdwhxu gh vhfrqg
ruguh +jdppd, gdqv od jhvwlrq gx sruwhihxlooh1
Oh frh!flhqw wkíwd
Oh wkíwd g*xqh rswlrq phvxuh od yduldwlrq dwwhqgxh gx sul{ gh fhwwh rswlrq vxu xqh frxuwh
sìulrgh/ gxh dx vhxo sdvvdjh gx whpsv1 Pdwkìpdwltxhphqw/ oh wkíwd hvw ìjdo ã od gìulyìh gx sul{
gh o*rswlrq sdu udssruw dx whpsv1
Frpph srxu oh ghowd/ lo hvw srvvleoh gh gìqlu oh wkíwd joredo g*xq sruwhihxlooh frpph ìwdqw od
vrpph ghv wkíwdv gh fkdtxh srvlwlrq gx sruwhihxlooh1
Xq wkíwd srvlwli vljqlh txh oh vlpsoh ìfrxohphqw gx whpsv hqwudñqhud xqh dxjphqwdwlrq gh
od ydohxu gx sruwhihxlooh/ hw lqyhuvhphqw1 Txdqg xq rsìudwhxu frqvwuxlw xqh srvlwlrq ghowd0qhxwuh/
lo shxw ìyhqwxhoohphqw xwlolvhu oh whpsv frpph vrxufh gh surw/ hq frqvwuxlvdqw xq sruwhihxlooh
ã wkíwd srvlwli1 Oh sureoëph ylhqw gx idlw txh/ oruvtx*xq sruwhihxlooh hvw jìuì hq ghowd0qhxwuh/ ohv
ydohxuv ghv frh!flhqwv wkíwd/ jdppd/ hw yìjd vrqw wuëv olìhv1 Od srolwltxh rswlpdoh srxu od jhvwlrq
g*xq sruwhihxlooh qh vhud grqf sdv wrxmrxuv od srvlwlylwì gx wkíwd1
Oh frh!flhqw jdppd
Oh jdppd g*xqh rswlrq/ qrwì / hvw od vhqvlelolwì gx ghowd ã o*dfwli vrxv0mdfhqw1 Lo v*h{sulph/
pdwkìpdwltxhphqw/ frpph od gìulyìh vhfrqgh gx sul{ gh o*rswlrq sdu udssruw dx frxuv gx vrxv0
mdfhqw1 Oruvtxh oh jdppd hvw idleoh/ ohv xfwxdwlrqv gx frxuv gx vrxv0mdfhqw q*rqw txh ghv hhwv wuëv
qìjoljhdeohv vxu oh ghowd1 Gdqv fh fdv/ lo qh vhud jxëuh qìfhvvdluh gh uìylvhu ohv srvlwlrqv gìwhqxhv
srxu pdlqwhqlu oh ghowd surfkh gx qlyhdx uhfkhufkì1 D o*lqyhuvh/ xqh srvlwlrq dyhf xq jdppd ìohyì
qìfhvvlwh xqh vxuyhloodqfh frqvwdqwh hw xqh uìylvlrq iuìtxhqwh gx sruwhihxlooh1
Frpph srxu oh ghowd hw oh wkíwd/ od qrwlrq gh jdppd v*dssoltxh ã xq sruwhihxlooh g*rswlrqv vxu
oh píph vrxv0mdfhqw/ oh jdppd joredo ìwdqw od vrpph ghv jdppdv gh fkdtxh rswlrq1
D xq lqvwdqw grqqì/ xq rsìudwhxu fkhufkh ã lqvhqvlelolvhu vrq sruwhihxlooh dx{ yduldwlrqv gh
pdufkì1 Fhwwh frxyhuwxuh uhvwh wuëv vrxyhqw lpsduidlwh/ hw lo v*djlw doruv gh phvxuhu oh ulvtxh uìvlgxho1
Oh jdppd hw oh wkíwd yrqw mrxhu fh u÷oh hw qrxv shuphwwuh gh gìfuluh qrwuh h{srvlwlrq dx ulvtxh1
Vfkìpdwltxhphqw/ lo h{lvwh wurlv frqjxudwlrqv srvvleohv srxu xqh srvlwlrq ghowd0qhxwuh =
Jdppd qìjdwli/ wkíwd srvlwli
Jdppd qhxwuh/ wkíwd srvlwli
Jdppd srvlwli/ wkíwd qìjdwli
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+d, Jdppd qìjdwli
+e, Jdppd qxo
+f, Jdppd srvlwli
Ilj1 4= Srvlwlrqv %ghowd0qhxwuh%
Ohv wurlv frqjxudwlrqv suìfìghqwhv pëqhqw ã ghv surov gh S)O glìuhqwv1 Fhv wurlv surov
vrqw uhsuìvhqwìv vxu od jxuh 4 =
Oh jdppd hvw qìjdwli +vrxv0jxuh 4+d,,1 Gdqv fh fdv/ oh phloohxu uìvxowdw vhud uìdolvì hq
devhqfh gh yduldwlrqv gx frxuv gh o*dfwlrq gh edvh1 Wrxwh xfwxdwlrq lqgxlw xqh edlvvh gx
S)O1 Qrwrqv/ gh soxv/ txh gdqv fhwwh frqjxudwlrq/ ohv shuwhv shxyhqw íwuh wuëv lpsruwdqwhv1
Oh jdppd hvw qxo +vrxv0jxuh 4+e,,1 Od srvlwlrq hvw jdppd0qhxwuh1 Oh uìvxowdw q*hvw jxëuh
dhfwì sdu ghv xfwxdwlrqv gx vrxv0mdfhqw1 Lo q*hvw sdv qìfhvvdluh g*dmxvwhu wuëv uìjxolëuhphqw
vrq sruwhihxlooh1
Oh jdppd hvw srvlwli +vrxv0jxuh 4+f,,1 Wrxwh xfwxdwlrq hvw vrxufh g*dpìolrudwlrq gh od
uhqwdelolwì gx sruwhihxlooh1 Oh uìvxowdw oh soxv pdxydlv hvw uìdolvì hq devhqfh gh xfwxdwlrq gx
frxuv gx vrxv0mdfhqw1 Gdqv fhwwh frqjxudwlrq/ oh ulvtxh hvw doruv olplwì1
D wlwuh g*h{hpsoh/ frqvlgìurqv o*ìyroxwlrq/ vxu xqh frxuwh sìulrgh/ g*xq sruwhihxlooh hq ghowd
qhxwuh/ jdppd srvlwli hw wkíwd qìjdwli1 Fh sruwhihxlooh hvw frqvwlwxì g*xqh rswlrq +srvlwlrq orqjxh,
hw gh vd frxyhuwxuh +srvlwlrq frxuwh,1 Od ydohxu gh o*rswlrq/ irqfwlrq gx vrxv0mdfhqw/ hvw uhsuìvhqwìh
vxu od jxuh 5+d, sdu od frxueh Sul{ hq w > od ydohxu gh od frxyhuwxuh hq ghowd0qhxwuh hvw uhsuìvhqwìh
sdu od frxueh Frxyhuwxuh hq ghowd1 Vxu xqh frxuwh sìulrgh/ ohv yduldwlrqv vxelhv sdu oh sruwhihxlooh
shxyhqw íwuh gìfrpsrvìhv hq ghx{ skìqrpëqhv =
o*rswlrq shug gh od ydohxu oruvtxh oh whpsv v*ìfrxoh +frxueh Sul{ hq w.w,/ lqgìshqgdpphqw
ghv prxyhphqwv gx pdufkì +wkíwd qìjdwli,1
wrxw prxyhphqw gx vrxv0mdfhqw hqwudñqh xqh dxjphqwdwlrq gh od ydohxu gx sruwhihxlooh +jdppd
srvlwli,/ fdu od ydohxu gx gìulyì vhud wrxmrxuv vxsìulhxuh ã od ydohxu gh od frxyhuwxuh1
Od uìvxowdqwh gh fhv ghx{ hhwv hvw uhsuìvhqwìh vxu ohv jxuhv 5+e, hw 4+f,1 Fh w|sh gh srvlwlrq
hqwudñqh xq jdlq oruv gh iruwv prxyhphqwv gh pdufkì +ã od kdxvvh rx ã od edlvvh, hw xqh shuwh gdqv
xq pdufkì wurs fdoph1
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+d, Hhw Wkíwd 0 Hhw Jdppd
+e, Uìvxowdw dwwhqgx
Ilj1 5= H{hpsoh gh frxyhuwxuh lpsduidlwh hq ghowd0qhxwuh hw jdppd srvlwli
Oh frh!flhqw yìjd
Oh yìjd g*xqh rswlrq/ qrwì &> hvw od vhqvlelolwì gx sul{ gh fhwwh rswlrq ã od yrodwlolwì gx vrxv0
mdfhqw1 O*lqwìuíw sruwì ã fhw lqglfdwhxu surylhqw gx idlw txh oh sul{ ghv rswlrqv hvw irqfwlrq gh
od yrodwlolwì1 Lo hvw píph srvvleoh gh gìgxluh ghv ydohxuv ghv rswlrqv vxu oh pdufkì xqh yrodwlolwì
lpsolflwh = ã fkdtxh sul{ revhuyì fruuhvsrqg xqh yrodwlolwì1 Fhwwh yrodwlolwì shxw doruv íwuh frqvlgìuìh
frpph xq idfwhxu gh ulvtxh ã sduw hqwlëuh/ grqw ohv xfwxdwlrqv vrqw revhuydeohv gluhfwhphqw vxu
oh pdufkì hw grqw lo ghylhqw oìjlwlph gh fkhufkhu ã vh frxyulu frqwuh ohv yduldwlrqv1 Oh yìjd shuphw
gh uìsrqguh/ hq sduwlh/ ã fh sureoëph hw gh txdqwlhu ohv yduldwlrqv gh od ydohxu g*xqh rswlrq gxhv
ã xq oìjhu prxyhphqw gh od yrodwlolwì1
Hq jìqìudo/ oh yìjd g*xq sruwhihxlooh hvw od vrpph ghv yìjdv ghv srvlwlrqv gh fh sruwhihxlooh1
Fhshqgdqw/ o*h{lvwhqfh vxu ohv pdufkìv g*rswlrqv gh soxvlhxuv yrodwlolwìv srxu xq píph vrxv0mdfhqw
vrxoëyh xqh lqfrkìuhqfh hqwuh ohv sul{ frqvwdwìv hw od wkìrulh fodvvltxh +rq sduoh qrwdpphqw gh
vploh gh yrodwlolwì,1 Dxvvl/ phvxuhu oh yìjd g*xq sruwhihxlooh uhylhqw ã phvxuhu o*h{srvlwlrq gh
qrwuh sruwhihxlooh ã xq dffurlvvhphqw jìqìudo gh wrxwhv ohv yrodwlolwìv1
Frpph srxu oh jdppd/ lo hvw srvvleoh g*dqqxohu vd vhqvlelolwì ã od yrodwlolwì1 Fhfl shuphw/ hqwuh
dxwuhv/ gh uìgxluh od gìshqgdqfh gh od ydohxu g*xq sruwhihxlooh ã xq sdudpëwuh gl!floh ã hvwlphu1
Sudwltxhphqw/ srxu dqqxohu oh yìjd/ rq dmrxwhud g*dxwuhv rswlrqv dx sruwhihxlooh1 Wrxwhirlv/ fhv
rswlrqv dxurqw ìjdohphqw xqh lqflghqfh vxu ohv dxwuhv lqglfdwhxuv +ghowd/ jdppd/111,1
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Oh frh!flhqw ukr
Ukr/ qrwì / uhsuìvhqwh od vhqvlelolwì g*xqh rswlrq dx wdx{ g*lqwìuíw xwlolvì gdqv ohv prgëohv
g*ìydoxdwlrq1 Fh sdudpëwuh hvw vxlyl xqltxhphqw srxu od frxyhuwxuh gh gìulyìv dfwlrqv hw lqglfhv1
Hq sudwltxh/ o*hqvhpeoh gh od frxueh ghv wdx{ hvw sulvh hq frpswh hw ukr uhsuìvhqwh doruv od vhqvlelolwì
ã xqh wudqvodwlrq gh o*hqvhpeoh gh fhwwh frxueh1 Fh sdudpëwuh uhyíw wrxwhirlv xqh lpsruwdqfh prlqv
fdslwdoh txh ohv dxwuhv vhqvlelolwìv suìflwìhv1
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Lgìdohphqw/ xq sruwhihxlooh ghyudlw íwuh sduidlwhphqw frxyhuw srxu v*dvvxuhu xq uhqghphqw txdvl0
phqw frqvwdqw hw vdqv ulvtxh1 Gdqv od sudwltxh/ fhwwh frxyhuwxuh sduidlwh hvw lpsrvvleoh1 Rq fkhufkh
doruv wrxw g*derug ã lppxqlvhu vrq sruwhihxlooh frqwuh ohv yduldwlrqv gx vrxv0mdfhqw +ghowd, sxlv gh
od yrodwlolwì +yìjd, txl vrqw frqvlgìuìv frpph ohv ulvtxhv gh suhplhu ruguh1 Uhvwh doruv xq fkrl{ ã
hhfwxhu hq fh txl frqfhuqh oh ulvtxh uìvlgxho1 Dlqvl/ hq irqfwlrq ghv dqwlflsdwlrqv gh od yrodwlolwì
gx pdufkì/ rq sulyloìjlhud xqh vwudwìjlh hq wkíwd srvlwli/ rü oh whpsv hvw xqh vrxufh gh surw/ rx
xqh vwudwìjlh hq jdppd srvlwli/ rü ohv yduldwlrqv gx pdufkì vrqw xqh vrxufh gh surw1
Srxu qlu/ fhv vhqvlelolwìv vrqw srxu od soxsduw wuëv olìhv1 Lo hvw dlqvl lpsrvvleoh gh {hu vlpxo0
wdqìphqw wrxwhv ohv vhqvlelolwìv g*xq sruwhihxlooh srxu v*dvvxuhu xq S)O srvlwli vdqv suhqguh gh
srvlwlrq1 Hq g*dxwuhv whuphv/ xq uhqghphqw soxv ìohyì hqwudñqh xq ulvtxh soxv lpsruwdqw1
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