Something like
select *
from mytable
where account in (select ext.account
from mytable ext
inner join (SELECT account, date
FROM mytable ext
WHERE OPEN_AMOUNT = 0
or OPEN_AMOUNT < gross_amount) sub
on ext.account = sub.account
and ext.date < sub.date
where open_amount > 0)
should do.
If you need something more like a chain control it'll be more difficoult.
Can you please specify the database you are using? Some db specific feature can actually help a lot.