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USST (     秽33櫃櫶___PPT10i.沸<Q+D=' = @B +"/ 6.P (   +  饃0 犊?肏5 Marcador de nmero de diapositiva^ `  餽*(  ;   饃6 秮0e槻0e槻?Rectangle 2 `}   餺'Modeling preferences under uncertainty ( (( 鹬   饃p1 秮0e槻0e槻?Rectangle 4 `  Which of these lotteries do you prefer?The EMV of A is 200 The EMV of B is 25000 Yet many subjects fear the high potential loss of 50000 and end up preferring A to B  + 餷  餌A??Picture 7}P   餳7 犊?81 Marcador de pie de pgina^   餸 DRI. USST (     秽33櫃櫶___PPT10i.旨鸠|+D=' = @B +" 瘀`$疝(  $+ $ 饃 2 犊?肏5 Marcador de nmero de diapositiva^ `  餽*(  : $  饃2 秮0e槻0e槻?Rectangle 2 `}   餹&Modeling preferences under uncertainty' ' '  $  饃9 秮0e槻0e槻?Rectangle 3 `餬 >6___PPT9 Consider this situation Throw a (balanced) coin until head appears. If this happens in the n-th draw, you get 2^n euros. How much are you ready to pay to enter in the game?? "   $ 餳; 犊?81 Marcador de pie de pgina^   餸 DRI. USST (     秽33櫃櫶___PPT10i.沸<Q+D=' = @B +"| 饆p(餭(  (+ ( 饃衖 犊?肏5 Marcador de nmero de diapositiva^ `  餽*(  : (  饃ph 秮0e槻0e槻?Rectangle 2 `}   餹&Modeling preferences under uncertainty' ' ' 饦 (  饃恖 秮0e槻0e槻?Rectangle 3 `餬 >6___PPT9 饐.Consider this situation Throw a (balanced) coin until head appears. If this happens in the n-th draw, you get 2^n euros. How much are you ready to pay to enter in the game?? The EMV of the game is 1+1+1+& . Yet most people would pay at most a few $ to enter in the game& & " `  ( 餳_ 犊?81 Marcador de pie de pgina^   餸 DRI. USST (     秽33櫃櫶___PPT10i.旨`&T+D=' = @B +" 痱,疒(  ,+ , 饃狕f悼?肏5 Marcador de nmero de diapositiva^ `  餽*(  ; ,  饃俐f祦0e槻0e槻?Rectangle 2 `}   餺'Modeling preferences under uncertainty ( ( (  ,  饃0g祦0e槻0e槻?Rectangle 4 `餬 >6___PPT9 瘘 Expected monetary value is not always an appropriate criterion for decision making under uncertaintyExpected utility provides an appropriate solution (at least normatively)  "   , 餳g悼?81 Marcador de pie de pgina^   餸 DRI. USST (     秽33櫃櫶___PPT10i.沸<Q+D=' = @B +"U \餞0<(  0+ 0 饃,g悼?肏5 Marcador de nmero de diapositiva^ `  餽*(  ; 0  饃(g祦0e槻0e槻?Rectangle 2 `}   餺'Modeling preferences under uncertainty ( ( ( 餻 0  饃p g祦0e槻0e槻?Rectangle 3]餬 >6___PPT9 館vA sketch of formalisation http://www.econ2.jhu.edu/people/karni/chapter.pdf Provides a rigorous description \ " ZU Z Z " Z Zw8   1 * @M 0 餳 !g悼?81 Marcador de pie de pgina^   餸 DRI. USST (     秽33櫃櫶___PPT10i.沸<Q+D=' = @B +"z 饄4餫(  4+ 4 饃*g悼?肏5 Marcador de nmero de diapositiva^ `  餽*(  : 4  饃!g祦0e槻0e槻?Rectangle 2 `}   餹&Modeling preferences under uncertainty' ' ' "  4  饃"g祦0e槻0e槻?Rectangle 3"癜 ┟ PK!瘅娀[Content_Types].xml攽蚃0秋傦*mi獹]`H6 橷w咿t?. g#¦踚3E掇).+浯7瞩 >諳N 庌憘1瑲藡z "+R 鱎hB.} /潖<芧霫轙窄赞%r〩K4uK~嶪耧龇0瞲諱 姠e玢`嚯|X}拏厌膽 躀`呓宽N4a〨2$猂KI焃)4(諱9`ヽtB{羴籀m:f@穈3悘n陓O拯纪,軛苧熊鬓劲j亲x⒐R0T ,0榆早@况闀}W﨎麹乾5vPK! %褻鳻drs/shapexml.xml靄蚽6;Y菐骻腨$A0#N鼻倴岲$碡9鮕鷋}拁$-藂`w兡3{萊鈭蝡f8?尜鏨柌┰&蒛7?韘&U攺u咤窟]餄pf琍#戞Jv鵟螉)>Vt冖觝榟,3a>鍏T鑻s 婫}(4RYa1Q6ZG峀$姛c(5}鞿淹疮Y2.ы#`唅oe$頢xc>溃桮f亴dFZhz拤帨Yべ:龠i#@碵\滥2燰t祆kr兓祦3併逴dl5 妃壋G-@o笞Dh蒠鷽橭涰6P楚鹊馉W{啱=j抅濠鐧PF韗薡h^Y<筓鎅!lO 娙旱谪毁 鏆垂cQH =cI*XO7Hj炖伪#_IL宆;勵a `9汩!潅Jx懆劙索J戅C頢蜦2昧觽庫6|#EO]O8W雎21 颥蔌腎 洫?Q& 腘z鷳eS乤 ^笖:(4CT盷-堍w8笿踺y8<-涀X踃D/@)=肶懾h|-$厊窗伷B夣聬勆 TZ1 Et@扣+Z5攦鑘0錫%YXu4{?燴A瑦砤鄰;閞)滄丈癝8{|鋎g鍁6^)愉I囈)m咦讁(K肹撡玊 ?6U畀石4 K oL&#饕u{%/A掷J; 玃2帯矺闘zjA鶋f仰籫 ?ej/祦蔙瑄H:"持R;9c=c{阜頬齓!5l蠋蹭忩咧1fGB擣m擵) 鵁dげ6#[菆`E稁'd@jr邶箩嵢殑H5 -酀#襶Gあ各@ 鐏悋颸荱} xC轭#牕'咤齇$份{遯}篇駳F7O6焞D篔!荋a曏哢HFj"#PZK埝)堉覻y%]V搴璎騛旈Z藅'S蟙塺^>Y股餼蓻5綯娗P<鎐U\P<齐镯('W猘6i`肉自賊厨X!媖W塇M1艕!<隳(Q岧b>>t欮襥簕 凹w鍈E7+x!y鵺,* 貅Gù厏3.誳啚Yy蕿%{瞮l∫/*齴且/拸毟塠菆?c曎 2 3 +O);S滲 烄雾擛D6P虬v蒀:驋O鴠B}煇膬膬腸鳓蚜7;)飦|兵刵妕7E.3爝~T6_崅kw藳l4霹PK!%县drs/downrev.xmlD徚N0 @颒麮d$n,e爥昬 樊混5^h拻d[俗cG鸜蟴矱o[q峸 nGr曌普 6弪DL4掇憘",鏃3痰?箓庪T 柛槪&.2V Y#邞c恩羈1訰<避秗渆i8衊G U_雰U3 錵f霍迼焽韹R譝#圖}?迆?郰狄2綗p威m 寜辮-S愺_PK-!瘅娀[Content_Types].xmlPK-!1輄a ._rels/.relsPK-! %褻鳻)drs/shapexml.xmlPK-!%县drs/downrev.xmlPK餬 >6___PPT9 餢DM expresses preferences over lotteries Preferences rational: transitive and complete Independence property Continuity property (no heaven, no hell) Preferences modeled through expected utility Utility is affine unique H( " Zn ZH Z Z 餷 4 餌A??Picture 4 @ 0 4 餳0.g悼?81 Marcador de pie de pgina^   餸 DRI. USST (     秽33櫃櫶___PPT10i.沸<Q+D=' = @B +" 鹪8鸺(  8+ 8 饃$g悼?肏5 Marcador de nmero de diapositiva^ `  餽*(  9 8  饃 ,g祦0e槻0e槻?Rectangle 2 `}   餸%Modeling preference. Single criteria & & & 痱 8  饃/g祦0e槻0e槻?Rectangle 3/  q  &VDetermine range of interest Assign utility 0 to worst value and utility 1 to best value Assign utilities to a few intermediate values (eg EP) Fit a utility function (e.g. through nonlinear least squares) Check for consistency Perform sensitivity analysisTake into account biases It. Imprecision Details http://www.jstor.org/pss/2631564 6, P+ " PVF ;     B5U 8 餳%g悼?81 Marcador de pie de pgina^   餸 DRI. USST (     秽33櫃櫶___PPT10i.沸<Q+D=' = @B +" 饜<饃(  <9 <  饃@0g祦0e槻0e槻?Rectangle 2 `}   餸%Modelling preferences. Risk attitudes& &(& 餡 < 餏`)g悼?Text Box 4P9$  疳a Risk aversion. Concave utility Risk proneness. Convex utility Risk neutrality. Linear utility 8a 2 2CaAb ; <  饃&g祦0e槻0e槻?Rectangle 5 `  餺 Three basic risk attitudes      < 餏0#g悼?Text Box 6 z 饢"Consequence varying risk attitudes# 2#C"    < 餳#g悼?81 Marcador de pie de pgina^   餸 DRI. USST (    + < 饃0g悼?肏2 Marcador de nmero de diapositiva^ `  餽*(   秽33櫃櫶___PPT10i. 沸1贊+D=' = @B +" 鸹@穑(  @# @  饃1g祦0e槻0e槻?Rectangle 2 `}   餡Risk attitudes  ( 鹑 @  饇A??Picture 6H\  @ 餏*g悼?Text Box 7 皓5Compare lotteries A and B. Which one do you prefer?6 26C5    @ 餳g悼?81 Marcador de pie de pgina^   餸 DRI. USST (    + @ 饃@%g悼?肏2 Marcador de nmero de diapositiva^ `  餽*(   秽33櫃櫶___PPT10i. 沸1贊+D=' = @B +" 馂D饐(  D# D  饃氨岜0e槻0e槻?Rectangle 2 `}   餡Risk attitudes  ( 鹑 D  饇A??Picture 6H\  D 餏翅笨?Text Box 7 皓5Compare lotteries A and B. Which one do you prefer?6 26C5   疔 D 餏`结笨?Text Box 8  餰If you prefer B to A, you seem to prefer the sure prize to the lottery (risk aversion)In such case, the expected utility of B should be bigger than that of A: * u(0) + * u(100000) = < 1 * u(50000) >X 2y  2CX  z  D 餳p瘁笨?81 Marcador de pie de pgina^   餸 DRI. USST (    + D 饃惛岜?肏2 Marcador de nmero de diapositiva^ `  餽*(   秽33櫃櫶___PPT10i. 沸唢+D=' = @B +" 馉H饒(  H# H  饃0丰眮0e槻0e槻?Rectangle 2 `}   餡Risk attitudes  ( 鹑 H  饇A??Picture 3H\  H 餏 滇笨?Text Box 4 皓5Compare lotteries A and B. Which one do you prefer?6 26C5   疠 H 餏喾岜?Text Box 5  餲If you prefer A to B, you seem to prefer the lottery to the sure prize (risk proneness)In such case, the expected utility of A should be bigger than that of B: * u(0) + * u(100000) = > 1 * u(50000) >Z 2y  2CZ  z  H 餳P漆笨?81 Marcador de pie de pgina^   餸 DRI. USST (    + H 饃欣岜?肏2 Marcador de nmero de diapositiva^ `  餽*(   秽33櫃櫶___PPT10i. 沸1贊+D=' = @B +" 鸲L馂(  L# L  饃轻眮0e槻0e槻?Rectangle 2 `}   餡Risk attitudes  ( 鹑 L  饇A??Picture 3H\  L 餏 泪笨?Text Box 4 皓5Compare lotteries A and B. Which one do you prefer?6 26C5   痼 L 餏玲笨?Text Box 5  饈If you are indifferent between A and B, you seem indifferent between the lottery and the sure prize (risk neutrality)In such case, the expected utilities of A and B should be equal: * u(0) + * u(100000) = = 1 * u(50000) >x 2q  2Cx  r  L 餳悽岜?81 Marcador de pie de pgina^   餸 DRI. USST (    + L 饃0箩笨?肏2 Marcador de nmero de diapositiva^ `  餽*(   秽33櫃櫶___PPT10i. 沸1贊+D=' = @B +"- 饏P餸(  P瘙 P  餽嗦岜0e槻0e槻?Ttulo 1 `}   8Risk attitudes 疝 P  饞A??0Marcador de contenido 5     P 餳惷岜?8Marcador de pie de pgina 3^   餸 DRI. USST (    + P 饃鹉岜?肏Marcador de nmero de diapositiva 4^ `  餽*(   秽33櫃櫶80___PPT10.虮悘蕩"   鸶 T馉 (  T" T  饃 轴眮0e槻0e槻?Rectangle 2 `}   餠Risk attitudes ( 痃 T 餏兄岜?Text Box 3S 9:  餼 ( 2CA 瘙 T  饃 酸眮0e槻0e槻?Rectangle 4 `  2 Formally, for a lottery (p1,x1;p2,x2;& ;pn,xn) consider its monetary expected value MEV p1*x1+p2*x2+& +pn*xn and its certainty equivalent CE u^{-1}(p1*u(x1)+p2*u(x2)+& +pn*u(xn)) If MEV>CE, risk aversion If MEV<CE, risk proneness If MEV=CE, risk neutrality PN P      +            N    T 餳提笨?81 Marcador de pie de pgina^   餸 DRI. USST (    + T 饃0歪笨?肏2 Marcador de nmero de diapositiva^ `  餽*(   秽33櫃櫶___PPT10i. 沸1贊+D=' = @B +" 瘌0X疣(  X8 X  饃慁毂0e槻0e槻?Rectangle 2 `}   餷$Modelling preferences. Risk Aversion% %(% 痃 X 餏綮笨?Text Box 3S 9:  餼 ( 2CA ( X  饃篱毂0e槻0e槻?Rectangle 4 `  餦 Risk premium=CE-EMV Absolute Risk Aversion.  u  (c)/u (c) Constant Absolute Risk Aversion. Exponential utility function.   ~  k  X 餳@潇笨?81 Marcador de pie de pgina^   餸 DRI. USST (    + X 饃狖毂?肏2 Marcador de nmero de diapositiva^ `  餽*(   秽33櫃櫶___PPT10i. 沸1贊+D=' = @B +" 瘕@\疱(  \+ \ 饃犈岜?肏5 Marcador de nmero de diapositiva^ `  餽*(  ) \  饃`柔眮0e槻0e槻?Rectangle 2 `}   餧Which risk attitude??   疬 \ 餏舍笨?Text Box 3S 9:  餴   2  \  饃郎岜0e槻0e槻?Rectangle 4 `  餒  餷 \ 餌A??Picture 6dZ鸫 \ 饘A??伱MC900323614[1]Picture 7MC900323614[1] g \ 餳@a笨?81 Marcador de pie de pgina^   餸 DRI. USST (     秽33櫃櫶___PPT10i.沸<Q+D=' = @B +"5 4鹎4P!!`鸠4(  `+ ` 饃3 犊?肏3 Marcador de nmero de diapositiva^ `  餽*(  1饁 0"`  `C (Group 3"]~ 痱 ` 餪D 秴烫?Rectangle 40"`  餤  饤/饉 >v  `C (Group 5"P"( 饐B ` 餠?Line 6 饐B  ` 餠?Line 7 饐B  ` 餠?Line 8{ 6 /  ` 餖> 秴?Text Box 9   皤90 300 620 900 1200*: 9C C:    ` 餘0? 秴?Text Box 10*F  饟1 0.8 0.6 0.4 0.2 0, 0ZC C   饒B  ` 餢?Line 11{ { 痤 ` 3 鹁@ABPCDE$FQ罭R*UVWXjJ? 0P @` 2*閈┿噺J ?7nJ 9v┿ L* PFreeform 120 痂 ` # 鸶@ABXCDE$FQ罭R*UVWXjJ? $4XXX0,$| @` 3Sp刢P[IRbT3 XFreeform 13: 痂 ` # 鸶@ABXCDE$FQ罭R*UVWX5%? $,\X @` 3~Rb蠗H![W伞{葂緅豋Y XFreeform 14{  鹗 ` C 饸@ABTCDE4FQ.RUVWXjJ? 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