Finding the minimum balance given a time frame

What is the best method by which I can calculate the minimum balance given a time frame? In my database, I have a deposit column and a withdraw column and date column at which they are done.

Update

Suppose on 1开发者_StackOverflow社区/1, the balance is 300. On 1/2, 300 is deposited with total of 600. On 1/15, 200 is withdrawn leaving a balance of 400. On 1/25, further withdrawal of 300 is made and the balance goes down to 100. On 1/28, 800 is deposited and balance total to 900. If on 1/31 I were to calculate the minimum balance for that month, I should get 100. Any ideas?

Use windowing functions to build the running balance, then extract the minimum out of each time interval like this:

with cte_transaction_data as
(
    select 300 as deposit, null as withdraw, date '01/02/2010' as transaction_date union all
    select null, 200, date '01/15/2010' union all
    select null, 300, date '01/25/2010' union all
    select 800, null, date '01/28/2010'
)
select
    month,
    min(balance) as minimum_balance
from
    (
        select 
            transaction_date,
            date_trunc('month', transaction_date) as month,
            300 
            + coalesce(sum(deposit) over(order by transaction_date rows between unbounded preceding and current row), 0)
            - coalesce(sum(withdraw) over(order by transaction_date rows between unbounded preceding and current row), 0) as balance
         from cte_transaction_data
    ) as running_balance
group by
    month
order by
    month

Result:

month                   minimum_balance
2010-01-01 00:00:00-06  100

Loop through each entry in the database for every day that there was a deposit/withdrawal and store the lowest number in a variable. If the number for the day being checked is lower, replace the variable with that number.