In the previous two examples, the random variable distributions were expressed as discrete outcome tables.  In this example, we will look at a model with distributions that are not discreet.  In particular, we will be using a normal distribution for our random variables.  Given the infinite number of outcomes in a normal distribution, we will also need to use @SPSAMPSIZE to declare the samples sizes to be used by the SP solver.  In addition, we will use @SPCORRPEARSON to input a correlation coefficient for some of the random variables.

In this example, we are investing to fund a college education (Birge and Louveaux, 1997).  We may invest in either stocks or bonds, both of which are assumed to have returns that are normally distributed as per the following table:

It also turns out that the returns on stocks and bonds are correlated, with a correlation coefficient of .5.

Our initial wealth is $55,000, while our target at the end of four periods is $80,000.  Our goal is to maximize wealth at the end of the three periods, however, we will be very disappointed if we don't meet our goal.  For this reason, we penalize ourselves by a factor of four for each dollar that we are short of our goal.  We also have the option of readjusting our portfolio at the start of each period.

The complete LINGO model can be found in the LINGO samples folder under the name SPCOLLEGENORM.LG4.