Which Shape For The Cost Curve of Risk? - Christian Gollier

to the shape of the cost curves. For instance, the properties of these curves ..... Under risk vulnerability, a zero0mean background risk reduces the demand.
273KB taille 19 téléchargements 271 vues
Zklfk Vkdsh Iru Wkh Frvw Fxuyh ri UlvnB Orxlv Hhfnkrxgw Fdwkrolf Xqlyhuvlw| ri Prqv Fkulvwldq Jroolhu JUHPDT dqg LGHL/ Xqlyhuvlw| ri Wrxorxvh/ dqg LXI1 Dsulo 4 @ Z Ef c ? ? @  ' ` A  Ef c  li devroxwh ulvn dyhuvlrq lv ghfuhdvlqj1 Surri= Zh nqrz wkdw @ .Ef n h +?@  ' .Ef n +h?3  `A  @ Ef c ?

49

dqg @ .Ef n +h?3  ` A  @ Ef c ? @ ' .Ef n +h?32  ` A  @ Ef c ?  `A  @ Ef  ` A  @ Ef c ?c ?  

Zh frqfoxgh wkdw @ Ef c ?c ?  2 ' `A  @ Ef c ? n ` A  @ Ef  `A  @ Ef c ?c ?   Vlqfh .h % ' f/ ` A  @ Ef c ?  f/ dqg GDUD lpsolhv wkdw; ` A  @ Ef  ` A  @ Ef c ?c ?    ` A  @ Ef c ?   Wkxv/ zh kdyh @ Ef c ?c ?  2  `A  @ Ef c ? n `A  @ Ef c ?   E| uhfxuuhqfh/ zh rewdlq @

 Ef c ?c ?  & 

& [

` A  @ Ef c ?   n 

'

Wkh idfw wkdw Z@ Ef c ? ' @ Ef c ?c f frqfoxghv wkh surri iru GDUD1 Wkh fdvh ri lqfuhdvlqj devroxwh ulvn dyhuvlrq lv rewdlqhg e| v|pphwu|1 Wkh frpelqdwlrq ri sursrvlwlrqv :dqg < gluhfwo| |lhogv wkh iroorzlqj fruro0 odu|= Fruroodu| 43 Lq wkh dgglwlyh prgho/ ulvn yxoqhudelolw| lpsolhv wkdw wkh zloo0 lqjqhvv wr sd| iru d ixoo holplqdwlrq ri wkh h{srvxuh wr ? l1l1g1 ulvnv lv odujhu wkdq ? wlphv wkh zloolqjqhvv wr sd| iru wkh ixoo holplqdwlrq wr wkh h{srvxuh ri d vlqjoh ulvn= Z@ Ef c ?  ?`A  @ Ef c  Surri= Uhphpehu wkdw GDUD lv qhfhvvdu| iru ulvn yxoqhudelolw|1 Wkxv/ e| Sursrvlwlrq q, ghfuhdvlqj lq } lv ohiw wr wkh uhdghu1

4:

Z@ Ef c ? 

? [

`A  @ Ef c 

'

E| Sursrvlwlrq :/ lw lpsolhv wkdw @

Z Ef c ? 

? [

`A  @ Ef c  ' ?` A  @ Ef c 

'

Wklv frqfoxghv wkh surri1

:

Frqfoxvlrq

Lqwxlwlrq vxjjhvwv wkdw ulvnv duh vhoi0djjudydwlqj iru ulvn0dyhuvh djhqwv/ l1h1 wkdw wkh frvw ri ulvn lv frqyh{ lq wkh qxpehu ri +lghqwlfdo, ulvn| h{srvxuhv1 Lq idfw/ lqwxlwlrq lv fohduo| frquphg rqo| lq wkh pxowlsolfdwlyh prgho zkhq wkh frvw ri ulvn lv phdvxuhg e| wkh frpshqvdwhg suhplxp1 Lq doo rwkhu fdvhv/ pruh uhvwulfwlrqv wkdq ulvn dyhuvlrq kdyh wr eh sxw rq wkh xwlolw| ixqfwlrq wr uhfryhu wkh lqwxlwlyh uhvxow1 Wkh frqglwlrqv uhtxluhg duh dozd|v ohvv ghpdqglqj iru wkh pxowlsolfdwlyh prgho wkdq iru lwv dgglwlyh frxqwhusduw1 Wkh| duh vxppdul}hg lq wkh iroorzlqj wdeoh1 Surshuw| Pxowlsolfdwlyh prgho Frpshqvdwlqj suhplxp vxshudgg1 dozd|v wuxh Ulvn suhplxp vxshudgglwlyh li GDUD ZWS lqfuhdvlqj li LUUD dqg GDUD Wdeoh 4= Surshuwlhv uhodwlqj wkh glhuhqw frqfhswv ri ZWS wr ulvn1

Dgglwlyh prgho li surshuqhvv li ulvn yxoqhudelolw| li ulvn yxoqhudelolw| wkh vl}h ri

Li rqh uhphpehuv wkdw wkh vxshudgglwlylw| ri wkh frvw ixqfwlrq grhv qrw qhfhvvdulo| lpso| dq hyhu|zkhuh lqfuhdvlqj pdujlqdo frvw/ wkh lqwxlwlyh lghd wkdw wkh pdujlqdo frvw ri ulvn vkrxog eh lqfuhdvlqj zlwk wkh qxpehu ri h{0 srvxuhv douhdg| dffxpxodwhg lq idfw lqgxfhv udwkhu vhyhuh uhvwulfwlrqv rq wkh vkdsh ri wkh xwlolw| ixqfwlrq1

4;

Uhihuhqfhv Duurz/ N1/ +4