In addition to what @chepner says, you can also use the for ... in style of for loop. This looks like:
for a in one two three; do
echo "${a}"
done
which would produce the result:
one
two
three
In other words, the list of words after the in part, separated by spaces, is looped over, with each iteration of the loop having a different word in the variable a.
To call your program 1000 times (or just modify to produce the list of arguments to run it once as in @chepner's answer) you could then do:
for a in $(seq 1 1000); do
./MyProgram $((RANDOM%200 - 100))
done
where the output of the seq command is providing the list of values to loop over. Although the traditional for loop may be more immediately obvious to many programmers, I like for ... in because it can be applied in lots of situations. A crude and mostly pointless ls, for example:
for a in *; do
echo "${a}"
done
for ... in is probably the bit of "advanced" bash that I find the most useful, and make use of it very frequently.
./MyProgram $( for ((i = 0; i < 1000; i++)); do echo $(($RANDOM%200-100)); done ). While only 1000 arguments isn't going to stress things, you will need to be careful if the argument list grows by a couple of orders of magnitude (100000 numbers is likely too big, or close to too big, to fit in the argument list).