The problem is that when you have a list in braces outside quotes, the shell performs Brace Expansion (bash manual, but ksh will be similar). Since the 'outside quotes' bit is important, it also tells you how to avoid the problem — enclose the string in quotes when printing:
#!/usr/bin/ksh
valid_data_range="{2013/05/01},{2013/05/02},{2013/05/03}"
finalDates="{$valid_data_range}"
print "$finalDates"
(The print command is specific to ksh and is not present in bash. The change in the assignment line is more cosmetic than functional.)
Also, the brace expansion would not occur in bash; it only occurs when the braces are written directly. This bilingual script (ksh and bash):
valid_data_range="{2013/05/01},{2013/05/02},{2013/05/03}"
finalDates="{$valid_data_range}"
printf "%s\n" "$finalDates"
printf "%s\n" $finalDates
produces:
ksh
{{2013/05/01},{2013/05/02},{2013/05/03}}
{2013/05/01}
{2013/05/02}
{2013/05/03}
bash (also zsh)
{{2013/05/01},{2013/05/02},{2013/05/03}}
{{2013/05/01},{2013/05/02},{2013/05/03}}
Thus, when you need to use the variable $finalDates, ensure it is inside double quotes:
other_command "$finalDates"
if [ "$finalDates" = "$otherString" ]
then : whatever
else : something
fi
Etc — using your preferred layout for whatever you don't like about mine.