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Modelling preferences under uncertainty. Utilities  q o(q   Fۿ?Text Box 3 7E :< David Ros david.rios@icmat.es Skype: david.rios.insua AXA-ICMAT Chair in ARA and Royal Academy of Sciences N\ 2N( 2 2CNCF\        {|  hէ޿?81 Marcador de pie de pgina^   m DRI. USST (    +  xPɧ޿?H2 Marcador de nmero de diapositiva^ `  r*(   33___PPT10i.P+D=' = @B +"g  (     rէށ0e0e?Ttulo 1 `}   1So far     ŧށ0e0e?0Marcador de contenido 2 `  ,Conceptual framework in RA IDs as problem structuring tool Probabilities for modeling uncertainty This deck Utilities for modeling preferences Xc $c ('   hϧ޿?8Marcador de pie de pgina 3^   r DRI. USST (    /  xѧ޿?HMarcador de nmero de diapositiva 4^ `  v* (   3380___PPT10." 0(  +  xȧ޿?H5 Marcador de nmero de diapositiva^ `  r*(  ;   x`֧ށ0e0e?Rectangle 2 `}   o'Modeling preferences under uncertainty ( ((    xҧށ0e0e?Rectangle 6 ` ~v___PPT9XP Build a function associating a number (utility) to each consequence, so that we compute the expected utility of each action u (a) = " u (a,) P ()  Optimal alternative: maximum expected alternative r " }c c b      5   hPԧ޿?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.<Q+D=' = @B +" @(  +  x@ǧ޿?H5 Marcador de nmero de diapositiva^ `  r*(  ;   xçށ0e0e?Rectangle 2 `}   o'Modeling preferences under uncertainty ( (( I   xʧށ0e0e?Rectangle 4 `  }'Which of these lotteries do you prefer?( (( l  DA??Picture 7}P   hħ޿?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.<Q+D=' = @B +" P (   +  xp޿?H5 Marcador de nmero de diapositiva^ `  r*(  :   xށ0e0e?Rectangle 2 `}   n&Modeling preferences under uncertainty' ' '    xށ0e0e?Rectangle 3 `b >6___PPT9 Consider this situation Throw a (balanced) coin until head appears. If this happens in the n-th draw, you get 2^n euros. How much are you ready to pay to enter in the game?? "    h޿?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.<Q+D=' = @B +" `$(  $+ $ x޿?H5 Marcador de nmero de diapositiva^ `  r*(  ; $  x ށ0e0e?Rectangle 2 `}   o'Modeling preferences under uncertainty ( ( (   $  xށ0e0e?Rectangle 4 `b >6___PPT9  Expected monetary value is not always an appropriate criteria for decision making under uncertainty Expected utility provides an appropriate solution (at least normatively)  "   $ h0޿?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.<Q+D=' = @B +"U \Tp(<(  (+ ( x ޿?H5 Marcador de nmero de diapositiva^ `  r*(  ; (  xށ0e0e?Rectangle 2 `}   o'Modeling preferences under uncertainty ( ( ( p (  xށ0e0e?Rectangle 3]b >6___PPT9 ^vA sketch of formalisation http://www.econ2.jhu.edu/people/karni/chapter.pdf Provides a rigorous description \ " ZU Z Z " Z Zw8   1 * }M ( h޿?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.<Q+D=' = @B +"z y,a(  ,+ , x޿?H5 Marcador de nmero de diapositiva^ `  r*(  : ,  xށ0e0e?Rectangle 2 `}   n&Modeling preferences under uncertainty' ' ' "  ,  xPށ0e0e?Rectangle 3" ê PK![Content_Types].xmlJ0*miG]`Hm6 Xwt?. g#Wi3E).+7 >ON ޑ1ˋz "+R RhB.} /<^ITխ%rHK4uK~I0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK! %CXdrs/shapexml.xml\n6;YǎgY$A0#NǂXD$9Yh}~$-q`wIJ3{Rpf8?Y&U7?s&Uu]pfP#Jv\Ί)>VStڢhh,3a>Ts G}(4RYa1Q6ZGL$c(5}ZʹY2.#`Dioe$Sxc>GځhzY:i#@[\į2Vtkr3Odl5 G-@oDhYO6PȵW{=j]PFrYh^Y۹qɛ5TDZ>tiʺ{ w}E7+x!yw,* G~3.zoYyʞ%{ul/*z/[Lj?c٪ 2 3 +O);SB @D6PvC:O}B}ăăc7;)|nt7E.3~T6_kw˛l4PK!%drs/downrev.xmlDN0 @HCd$n,ee 5^hd[cGYzEo[qw nGr 6DL4ޑ",3̵?T &.2V Y#ߑcb1R<ܶrei8`G U_U3 kf˻ޗRW#D}?~?Y2pm p-S_PK-![Content_Types].xmlPK-!1_a ._rels/.relsPK-! %CX)drs/shapexml.xmlPK-!%drs/downrev.xmlPKb >6___PPT9 XDM expresses preferences over lotteries Preferences rational: transitive and complete Independence property Continuity property (no heaven, no hell) Preferences modeled through expected utility Utility is affine unique H( " Zn ZH Z Z l , DA??Picture 4 @ 0 , hЭ޿?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.<Q+D=' = @B +" 0(  0+ 0 x޿?H5 Marcador de nmero de diapositiva^ `  r*(  9 0  xށ0e0e?Rectangle 2 `}   m%Modeling preference. Single criteria & & &  0  x`ށ0e0e?Rectangle 3/  q  &VDetermine range of interest Assign utility 0 to worst value and utility 1 to best value Assign utilities to a few intermediate values (eg EP) Fit a utility function (e.g. through nonlinear least squares) Check for consistency Perform sensitivity analysis Take into account biases It. Imprecision Details http://www.jstor.org/pss/2631564 6, P+ " PVF ;     5U 0 h޿?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.<Q+D=' = @B +" 4x(  49 4  xށ0e0e?Rectangle 2 `}   m%Modelling preferences. Risk attitudes& &(& W 4 F޿?Text Box 4P9$  a Risk aversion. Concave utility Risk proneness. Convex utility Risk neutrality. Linear utility 8a 2 2CaAb ; 4  xށ0e0e?Rectangle 5 `  o Three basic risk attitudes      4 F௧޿?Text Box 6 z "Consequence varying risk attitudes# 2#C"    4 hP޿?81 Marcador de pie de pgina^   m DRI. USST (    + 4 xТ޿?H2 Marcador de nmero de diapositiva^ `  r*(   33___PPT10i. 1ٝ+D=' = @B +" 8(  8# 8  xp§ށ0e0e?Rectangle 2 `}   WRisk attitudes  (  8  |A??Picture 6H\  8 F`޿?Text Box 7 5Compare lotteries A and B. Which one do you prefer?6 26C5    8 hP޿?81 Marcador de pie de pgina^   m DRI. USST (    + 8 x@޿?H2 Marcador de nmero de diapositiva^ `  r*(   33___PPT10i. 1ٝ+D=' = @B +"  <o(  <# <  xށ0e0e?Rectangle 2 `}   WRisk attitudes  (  <  |A??Picture 6H\  < F޿?Text Box 7 5Compare lotteries A and B. Which one do you prefer?6 26C5    < F ç޿?Text Box 8  NIf 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) Graphically& >X 2  2CX    < h޿?81 Marcador de pie de pgina^   m DRI. USST (    + < x޿?H2 Marcador de nmero de diapositiva^ `  r*(   33___PPT10i. +D=' = @B +"  @s(  @# @  xށ0e0e?Rectangle 2 `}   WRisk attitudes  (  @  |A??Picture 3H\  @ F@޿?Text Box 4 5Compare lotteries A and B. Which one do you prefer?6 26C5    @ Fp޿?Text Box 5  RIf 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) Graphically& >Z 2  2CZ    @ h޿?81 Marcador de pie de pgina^   m DRI. USST (    + @ xp޿?H2 Marcador de nmero de diapositiva^ `  r*(   33___PPT10i. 1ٝ+D=' = @B +"  D(  D# D  xށ0e0e?Rectangle 2 `}   WRisk attitudes  (  D  |A??Picture 3H\  D F0޿?Text Box 4 5Compare lotteries A and B. Which one do you prefer?6 26C5    D F޿?Text Box 5  ~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) Graphically& >x 2}  2Cx  ~  D h0޿?81 Marcador de pie de pgina^   m DRI. USST (    + D x޿?H2 Marcador de nmero de diapositiva^ `  r*(   33___PPT10i. 1ٝ+D=' = @B +"- Hm(  H H  r0ŧށ0e0e?Ttulo 1 `}   8Risk attitudes  H  A??0Marcador de contenido 5     H hƧ޿?8Marcador de pie de pgina 3^   m DRI. 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Risk AversionWhich risk attitude??Presentacin de PowerPoint-Multicriteria preferences under uncertainty -Multicriteria preferences under uncertainty Presentacin de PowerPoint Wrapping up Fuentes usadasTemaServidores OLE incrustadosTtulos de diapositivaL 8@ _PID_HLINKSAH2http://www.econ2.jhu.edu/people/karni/chapter.pdf!http://www.jstor.org/pss/2631564mailto:david.rios@icmat.esmailto:david.rios@icmat.es2http://www.econ2.jhu.edu/people/karni/chapter.pdf!http://www.jstor.org/pss/2631564mailto:david.rios@icmat.es,https://www.youtube.com/watch?v=gWUi3gHRPVA,https://www.youtube.com/watch?v=gWUi3gHRPVAmailto:david.rios@icmat.es,https://www.youtube.com/watch?v=gWUi3gHRPVA,https://www.youtube.com/watch?v=gWUi3gHRPVA_'DavidDavid  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrsuvwxyz{}~Root EntrydO)Pictures3Current User|SummaryInformation(PowerPoint Document('DocumentSummaryInformation8tRoot EntrydO)=g@Pictures3Current User,SummaryInformation(      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrsuvwxyz{_'DELLDELL