Resources

Oil Wildcatter's Problem in Risk Averse Setting

 /**************************************************************/
 /*          S A S   S A M P L E   L I B R A R Y               */
 /*                                                            */
 /*    NAME: DTREEE02                                          */
 /*   TITLE: Oil Wildcatter's Problem in Risk Averse Setting   */
 /*          (dtreee02)                                        */
 /* PRODUCT: OR                                                */
 /*  SYSTEM: ALL                                               */
 /*    KEYS: DTREE                                             */
 /*   PROCS: DTREE, PRINT, FORMAT, GPLOT                       */
 /*    DATA:                                                   */
 /*                                                            */
 /* SUPPORT:                             UPDATE:               */
 /*     REF: Example 2 from the DTREE chapter                  */
 /*    MISC:                                                   */
 /*                                                            */
 /**************************************************************/

 goptions hpos=80 vpos=32;

/* -- create the STAGEIN= data set                 -- */
data Dtoils4;
format _STNAME_ $12. _OUTCOM_ $15. _SUCCES_ $12.;
input _STNAME_ $ _STTYPE_ $ _OUTCOM_ $
    _SUCCES_ $ ;
datalines;
Divestment      Decision    No_Divestment      Insurance
.               .           10%_Divestment     Insurance
.               .           20%_Divestment     Insurance
.               .           30%_Divestment     Insurance
.               .           40%_Divestment     Insurance
.               .           50%_Divestment     Insurance
.               .           60%_Divestment     Insurance
.               .           70%_Divestment     Insurance
.               .           80%_Divestment     Insurance
.               .           90%_Divestment     Insurance
.               .           100%_Divestment    .
Insurance       Decision    Buy_Insurance      Cost
.               .           Do_Not_Buy         Cost
Cost            Chance      Low                Oil_Deposit
.               .           Fair               Oil_Deposit
.               .           High               Oil_Deposit
Oil_Deposit     Chance      Dry                .
.               .           Wet                .
.               .           Soaking            .
;

/* -- create the PROBIN= data set                         -- */
data Dtoilp4;
input _EVENT1 $ _PROB1  _EVENT3 $ _PROB3 ;
datalines;
Low         0.2     Dry         0.5
Fair        0.6     Wet         0.3
High        0.2     Soaking     0.2
;

/* -- create the PAYOFFS= data set                        -- */
data Dtoilu4(drop=i j k l);
length _STATE1-_STATE4 $16. ;
format _VALUE_ dollar12.0;

/* define and initialize arrays */
array DIVEST{11}  $16. _TEMPORARY_ ('No_Divestment',
                                    '10%_Divestment',
                                    '20%_Divestment',
                                    '30%_Divestment',
                                    '40%_Divestment',
                                    '50%_Divestment',
                                    '60%_Divestment',
                                    '70%_Divestment',
                                    '80%_Divestment',
                                    '90%_Divestment',
                                    '100%_Divestment'  );
array INSUR{3} $16.    _TEMPORARY_ ('Do_Not_Buy',
                                    'Buy_Insurance',
                                    ' '                );
array COST{4} $        _TEMPORARY_ ('Low',
                                    'Fair',
                                    'High',
                                    ' '                );
array DEPOSIT{4} $     _TEMPORARY_ ('Dry',
                                    'Wet',
                                    'Soaking',
                                    ' '                 );

do i=1 to 10;            /* loop for each divestment */
   _STATE1=DIVEST{i};

   /*
    * determine the percentage of ownership retained
    * for this scenario
    */
   PCT=1.0-((i-1)*0.1);

   do j=1 to 2;       /* loop for insurance decision */
      _STATE2=INSUR{j};

      /*
       * determine the premium need to pay for this
       * scenario
       */
      if _STATE2='Buy_Insurance' then PREMIUM=130000;
      else                            PREMIUM=0;

      do k=1 to 3;        /* loop for each well cost */
         _STATE3=COST{k};

         /* determine the cost for this scenario */
         if      _STATE3='Low' then  _COST_=150000;
         else if _STATE3='Fair' then _COST_=300000;
         else                        _COST_=500000;

         do l=1 to 3;  /* loop for each deposit type */
            _STATE4=DEPOSIT{l};

            /*
             * determine the oil deposit and the
             * corresponding net payoff for this scenario
             */
            if      _STATE4='Dry' then _PAYOFF_=0;
            else if _STATE4='Wet' then _PAYOFF_=700000;
            else                       _PAYOFF_=1200000;

            /* determine redeem received for this scenario */
            if _STATE2='Buy_Insurance' and _STATE4='Dry' then
                 REDEEM=200000;
            else REDEEM=0;

            /* calculate the net return for this scenario */
            _VALUE_=(_PAYOFF_-_COST_-PREMIUM+REDEEM)*PCT;

            /* drop unneeded variables */
            drop _COST_ _PAYOFF_ PREMIUM REDEEM PCT;

            /* output this record */
            output;
         end;
      end;
   end;
end;

/* output an observation for the scenario 100%_Divestment */
_STATE1=DIVEST{11};
_STATE2=INSUR{3};
_STATE3=COST{4};
_STATE4=DEPOSIT{4};
_VALUE_=0;
output;

run;

 /* -- print the payoff table                              -- */
title "Oil Wildcatter's Problem";
title3 "The Payoffs";
proc print data=Dtoilu4;
run;


/* -- PROC DTREE statements                               -- */
title "Oil Wildcatter's Problem";

proc dtree stagein=Dtoils4
           probin=Dtoilp4
           payoffs=Dtoilu4
           criterion=maxce rt=1200000
           nowarning;
   evaluate;
   summary / target=Divestment;
   summary / target=Insurance;
quit;


   /*  create a data set for the return corresponds to each */
   /*  divestment possibilities and the insurance options   */
data Data2g;
   input  INSURE DIVEST VALUE;
   datalines;
       1       0   45728
       0       0   44499
       1      10   46552
       0      10   48021
       1      20   46257
       0      20   49907
       1      30   44812
       0      30   50104
       1      40   42186
       0      40   48558
       1      50   38350
       0      50   45219
       1      60   33273
       0      60   40036
       1      70   26927
       0      70   32965
       1      80   19284
       0      80   23961
       1      90   10317
       0      90   12985
       1     100       0
       0     100       0
;

   /* -- define a format for INSURE variable             -- */
proc format;
   value sample 0='Do_Not_Buy' 1='Buy_Insurance';
run;

   /* -- define title                                    -- */
title h=3 "Oil Wildcatter's Problem";

   /* define legend                                      -- */
legend1 frame cframe=white label=none
        cborder=black position=center ;

   /* define symbol characteristics of the data points      */
   /* and the interpolation line for returns vs divestment  */
   /* when INSURE=0                                         */
symbol1 c=cyan i=join v=dot l=1 h=1;

   /* define symbol characteristics of the data points      */
   /* and the interpolation line for returns vs divestment  */
   /*  when INSURE=1                                        */
symbol2 c=green i=join v=square l=2 h=1;

   /* -- define axis characteristics                     -- */
axis1 minor=none label=('Divestment (in percentage)');
axis2 minor=none label=(angle=90 rotate=0 'Certainty Equivalent');

   /* set graphics options                                  */
goptions htext=1.5;

   /* plot VALUE vs DIVEST using INSURE as third variable   */
proc gplot data=Data2g ;
   plot VALUE*DIVEST=INSURE / haxis=axis1
                              vaxis=axis2
                              legend=legend1
                              name="dt2"
                              frame
                              cframe=white ;
   format INSURE SAMPLE.;
run;

quit;