Toward a Systematic Approach to the Economic ... - Christian Gollier

second-order stochastic dominance is an example of an unconditional risk comparison. ... wealth of an agent who does not purchase the contract, оi is the random .... Other forms of conditional stochastic dominance could be considered.
264KB taille 2 téléchargements 279 vues
AL@h_ @ 5)t|i4@|U TThL@U |L |i ,UL?L4U ,giU|t Lu N?Uih|@?|) WG L4T@h?} +t!t  ht|@? BwwW,+ N?iht|) Lu AL*Lti *it 5 kWww N?iht|) Lu U}@? }t| bbe



Wklv sdshu zdv zulwwhq zkloh Nlpedoo zdv d ylvlwru dw LGHL/ Xqlyhuvlw| ri Wrxorxvh1 Ilqdqfldo vxssruw iurp wkh IIVD dqg wkh +X1V1, Qdwlrqdo Vflhqfh Irxq0 gdwlrq lv judwhixoo| dfnqrzohgjhg1

Mt|h@U| 5iUL?_Lh_ih t|LU@t|U _L4?@?Ui @?tiht |i ^it|L? RN?_ih @| UL? _|L?t ** @** ht!@ihti @}i?|t Thiuih %  2 |L % q L?t_ih |i uL**L?} hi*@|i_ ^it|L?G RN?_ih @| UL?_|L?t ** @** ht!@ihti @}i?|t L Thi uih *L||ih) %  |L @ hiuihi?Ui *L||ih) /  @*tL Thiuih *L||ih) % 2 |L |@| hiuihi?Ui *L||ih)q ,@U Lu |iti |L ^it|L?t t @? i @4T*i Lu @ MhL@_ U@|i}Lh) Lu ^it|L?t Lu }hi@| hi*i@?Ui uLh |i iUL?L4Ut Lu ht! Ai tiUL?_ ^it|L? t @? i @4T*i Lu @ UL?_|L?@* ht! UL4T@htL?c *i |i ^it|L? Mi?_ tiUL?_Lh_ih t|LU@t|U _L4?@?Ui t @? i @4T*i Lu @? ?UL?_|L?@* ht! UL4T@htL? Ai t|LU@t|U Lh_ih @ht?} uhL4 @ UL?_|L?@* ht! UL4T@htL? t LMLt*) i@!ih |@? |@| @ht?} uhL4 |i ULhhitTL?_?} ?UL?_|L?@* ht! UL4T@htL?c M| i tL |@| |i |L t|LU@t|U Lh_iht @hi U*Lti*) hi *@|i_c tL |@| |i @?tih |L @? ?UL?_|L?@* ht! UL4T@htL? ThLM*i4 @*@)t ThL_it |i @?tih |L |i ULhhitTL?_?} UL?_|L?@* ht! UL4T@htL? ThLM *i4 W? @__|L? |L tL?} |i UL??iU|L? Mi|ii? T@h@**i* UL?_|L?@* @?_ ?UL?_|L?@* ht! UL4T@htL? ThLM*i4tc i @h|U*@|i @ 4i|L_ uLh tL*?} ML| !?_t Lu ThLM*i4t t?} |i RM@tt @TThL@U Ai M@tt @TThL@U @t Lu|i? Mii? ti_ 4T*U|*)c M| i @h}i |@| |ihi t @*i |L 4@!?} |t ti i T*U|c T@h|U*@h*) ? ?_U@|?} U ?ic ThiLt*) ?tL*i_ ThLM*i4t U@? hi@_*) Mi tL*i_ M) |i M@tt @TThL@U @?_ U U@??L|



W?|hL_U|L?

W? ii? |t U*@ttU@*c L?i4@??Lh}i?t|ih? uLh4*@|L?c *i| @*L?i |t 4Lhi hiUi?| i |i?tL?t ?|L ?L?i TiU|i_|*|) |iLhitc |i iUL?L4Ut Lu ?Uih|@?|) i?UL4T@ttit @ *@h}i ?4Mih Lu tii4?}*) _tT@h@|i hit*|t i U@ti |i iUL?L4Ut Lu ?Uih|@?|) t @ |iU?U@**) _U*| €i*_c @?_ |t hit*|t @hi ThLi_ ? @ _i @hi|) Lu @)tc @ tMt|@?|@* igLh| @t Mii? hi^hi_ |L *i@h? @| t Mi?_ @** Lu |t 4@Lh hit*|t i hit*|t @i Mii? _tULihi_ @?_ Lh!i_ L| ? @ @) @?@*L}Lt |L @?_Uh@u|?} M) @ t!**i_ @h|t@? `i ThLTLti @ *L?}|ih4 ThLiU|c Lu U |t T@Tih t @ M@hi Mi}? ??}c @4i_ @| t)t|i4@|3?} |i iUL?L4Ut Lu ?Uih|@?|) 5)t|i4@|3?} ?L*it U*@hu)?} UL??iU|L?t @4L?} hit*|t @?_ U@|i}Lhit Lu hit*|tc Lh}@ ?3?} @| t !?L? ?|L @hh@)t |@| hii@* M) UL?tTULt }@Tt @| t )i| ?!?L?c @?_ t|@?_@h_3?} 4i|L_t Lu _tULih) @?_ ThLLu ihuiU| Lh_ih t ?i|ih @||@?@M*i ?Lh _ith@M*ic M| Lh}@?3@|L? @?_ UL?tL*_@|L? @*L?} L?i _4i?tL? U@? uLt|ih Uhi@||) @*L?} L|ih _4i?tL?t @h| W Lu |t *L?}|ih4 ThLiU| t |i @||i4T| |L t)t|i4@|3i |i UL4 T@htL? Lu ht!tQitTiU@**) hit*|t hi*@|i_ |L t|LU@t|U _L4?@?Ui Ai ThLM*i4 Lu t|LU@t|U _L4?@?Ui t @ t|@?_@h_ L?i ? |i *|ih@|hi Lu t|@|t |Utc LTih@|L?t hiti@hU @?_ iUL?L4Ut W? iUL?L4Utc | @t €ht| i @4?i_ M) O@_@h @?_ +tti* dbSboc O@?LU @?_ wi) dbSbo @?_ +L|tU*_ @?_ 5|}*|3 db.fcb.o W? 4@?) ?t|@?Uitc 4@!?} @? @TThLTh@|i Lh_ih?} Lu ?Uih|@? ThLtTiU|t ML*t _L? |L |i ThLM*i4 Lu €?_?} |i hit|hU|L? L? |i h@?_L4 @h@M*it %   @?_ %  2 tU |@| .sE %2   .sE % 

E?UL?_|L?@* UL4T@htL?

E

uLh @?) u?U|L? s Mi*L?}?} |L tL4i ti|  c ihi . _i?L|it |i i TiU|@|L? LTih@|Lh 6Lh i @4T*ic u  t |i ti| Lu ?Uhi@t?} @?_ UL?U@i u?U|L?tc i }i| |i i**!?L? tiUL?_Lh_ih t|LU@t|U _L4?@?Ui Lh_ih E55# Wu s hiT hiti?|t @ |*|) u?U|L?c |t Lh_ih t tiu* |L _i|ih4?i i|ih @ U@?}i ? ht! t ?@?4Lt*) hiiU|i_ ? |i TLT*@|L? Lu ht!@ihti ?__@*t Wu s hiThiti?|t 4@h}?@* |*|)c |t Lh_ih t hi*i@?| |L _i|ih4?i i|ih ht! @ihti @?_ Th_i?| @}i?|t ?@?4Lt*) ?Uhi@ti |ih ThiU@|L?@h) t@?} ? |i u@Ui Lu @ U@?}i ? u|hi ?UL4i ht!t @?) L|ih ti|t Lu u?U|L?t  @i Mii? UL?t_ihi_ ? |i *|ih@|hic *i@_?} |L L|ih t|LU@t|U Lh_ih?}t 

@t uLh i @4T*i €ht|Lh_ih E65# Lh |h_Lh_ih EA5# t|LU@t|U _L4?@?Ui Lh_iht W? |t T@Tihc i ?it|}@|i @?L|ih |)Ti Lu t|LU@t|U _L4?@?Ui Lh_ih ?}t +@|ih |@? UL?t_ih?} |i ThLM*i4 i Thitti_ M) i^@|L? Ec i UL?t_ih |i uL**L?} ThLM*i4G ?_ih U UL?_|L? L? %   @?_ % 2 U@? i }@h@?|ii |@| .sE %   .s E /

',

.sE %2   .sE /

EUL?_|L?@* UL4T@htL? E2 uLh @ }i? hiuihi?Ui *L||ih) /  @?_ uLh @?) s Mi*L?}?} |L tL4i ti|   `i ?U*_i ? |t |)Ti @** L|ih ThLM*i4t ? U |i €ht| @?_%Lh tiUL?_ ? i^@*|) t hiT*@Ui_ M) @? i^@*|) L?_|L?@* ht! UL4T@htL?t @i 4@?) tiu* @TT*U@|L?t AL t|@h| |c UL?t_ih |i UL?_|L?@* ThLM*i4 T@h@**i* |L 55# W?t|i@_ Lu hi^h?} ?@?4|) Lu Thiuihi?Uit uLh %   Lih %  2 ? |i L*i TLT*@|L? Lu ht!@ih|iht E@? ?UL?_|L?@* ht! UL4T@htL?c i hi ^hi |@| @** |Lti L Thiuih % |L |i hiuihi?Ui *L||ih) /  Thiuih %  2 |L /  E@ UL?_|L?@* ht! UL4T@htL? Wu % 2 t 55#_L4?@|i_ M) %   c tU @ ThLT ih|) t @|L4@|U@**) t@|t€i_ | | t i@t) |L €?_ @ U@?}i ? _t|hM|L? |@| t@|t€it |i *@||ih ThLTih|) |L| Mi?} 55# Atc |i UL?_|L?@* UL?|ihT@h| |L 55# t i@!ih |@? 55# |ti*u L?_|L?@* ht! UL4T@htL? ThLM*i4t @*tL @i @TT*U@|L?t ? 4@h!i| ?}c ?_t|h@* Lh}@?3@|L? @?_ TL*|U@* iUL?L4) 6Lh i @4T*ic UL?t_ih |i ThLM*i4 Lu @ 4@?@}ih Lu @? ?th@?Ui UL4T@?) L L*_ *!i |L U@?}i |i Lgihi_ UL?|h@U| |L| *Lt?} Ut|L4iht W? |t i @4T*ic /  t |i h@?_L4 i@*| Lu @? @}i?| L _Lit ?L| ThU@ti |i UL?|h@U|c %   t |i h@?_L4 i@*| | |i ?|@* UL?|h@U| ETLttM*) | T@h|@* ?th@?Ui @?_ @? ? u@h Thi44c %  2 t |i ?i UL?|h@U| @?_ s t 4?t |i |*|) u?U|L?  q L| Bi? ht! @ihtL?c _Lit %  2 ?ii_ |L Mi @? 55#4ThLi4i?| Lih % ?iUitt@h*)c MiU@ti |i ThU@ti Lu |i ?|@* UL?|h@U| @**Lt 4 |L i |h@U| tL4i ?uLh4@|L? @ML| |i ht! Thiuihi?Uit Lu t Ut|L4iht 6Lh i @4T*ic u |i ?|@* TL*U) @t @ Thi44 4U *@h}ih |@? |i @U|@h@* @*ic L?*) }*) ht!@ihti @}i?|t ** @i ThU@ti_ | Ai ?th@?Ui UL4 T@?) U@? _it}? |i ?i UL?|h@U| M) t?} |@| ?uLh4@|L? Ai ti| Lu |i UL4T@?)