/*
** *********************************************************************
**  
** Version 20/06/04 KCDN (QFE 2nd edition)
** ---------------------
**
** How much you pay to avoid a fair bet ? 
** Certainty equivalent for power utility is the solution for xx from:
**
**     	(C-xx)^(1-gam)   =  1/2/ { (c+y)^1-gam  + (c-y)^1-gam }   	
** *********************************************************************
*/

new; cls ; screen off ; 
format /m1/rd 10,4 ;  outwidth 255 ; output on ;


@ ------------------------- True values of parameters ----------------------- @
gam = 2|10|50|100|250 ;		    @ --- alternative crra for power utility --- @
y = 10|100|1000|10000|20000 ;       @ --- alternative size of fair bet: prob win = 1/2 --- @ 

c = 50000 ;


@ --------------------------------------------------------------------------- @

w = c + y ; 

xx = zeros(rows(y),rows(gam) ) ;
i =1 ;
k = 1 ;

do until i > rows(gam) ;
   z = 1 - ( ( 0.5.*(1+y./c)^(1-gam[i]) +0.5.*(1-y./c)^(1-gam[i]) ) )^(1/(1-gam[i])) ;
   @ --- xx is the certainty equivalent of the fair bet: i.e. how much you would pay to avoid the bet --- @  
   xx[.,k] = z.*c ;			

   k = k+1 ;
   i = i+1 ;
endo ;

/* 
** *****************************************************
**                       Output 
** *****************************************************
*/
screen on ; 
mask1 = 1~1~1~1~1 ; 
let fmt1[5,3] = 
     "*.*lf" 32 4 
     "*.*lf" 13 4 
     "*.*lf" 13 4 
     "*.*lf" 13 4 
     "*.*lf" 13 4 ; 
run_table1 = gam' ; 

mask2 = 1~1~1~1~1~1~1 ; 
let fmt2[7,3] = 
     "*.*lf" 4 0      
     "*.*lf" 15 4 
     "*.*lf" 13 4 
     "*.*lf" 13 4 
     "*.*lf" 13 4 
     "*.*lf" 13 4 
     "*.*lf" 13 4 ; 
run_table2 = seqa(1,1,rows(y))~y~xx ; 

print "                    How Much Should One Pay For a Fair Bet ? " ; 
print "                    ======================================== " ; 
print ; 
print ; 
print "         Amount of the " ; 
print "            fair bet                            Rows of gam " ;  
print " ------------------------------------------------------------------------------------ "; 
call printfm(run_table1, mask1, fmt1) ; print ; 
print " ------------------------------------------------------------------------------------ "; 
call printfm(run_table2, mask2, fmt2) ; print ; 

end ;