Tracking payments on invoices - postgresql

Question

I am trying to track payments made by customers using the following tables:
CREATE TABLE IF NOT EXISTS invoices
(
id integer NOT NULL DEFAULT nextval('invoices_id_seq'::regclass),
customer_id integer NOT NULL
)
CREATE TABLE IF NOT EXISTS invoice_entries
(
id integer NOT NULL DEFAULT nextval('invoice_entries_id_seq'::regclass),
price numeric,
invoice_id integer NOT NULL
)
CREATE TABLE IF NOT EXISTS customer_transactions
(
id integer NOT NULL DEFAULT nextval('customer_transactions_id_seq'::regclass),
total_amount numeric NOT NULL,
invoice_id integer,
customer_id integer NOT NULL,
)
My problem is that a payment can be made to the customer's account, OR, it could be made to a specific invoice.
My goal is to generate aggregated columns that show the running balance, as well as the amount paid on any given invoice. If the payment was made directly to the customer's account, it will apply to any remaining balances on each invoice.
So far I have gotten this far:
WITH RECURSIVE CTE_R AS (
SELECT
ROW_NUMBER() OVER (PARTITION BY ct.customer_id) AS row_id,
pb.invoice_balance,
pb.invoice_id,
ct.total_amount
FROM customer_invoice_balances() as pb
LEFT JOIN customer_transactions as ct ON ct.customer_id = pb.customer_id
),
CTE AS (
SELECT
row_id,
invoice_balance,
invoice_id,
total_amount,
invoice_balance AS remaining_balance,
0::numeric AS amount_paid
FROM CTE_R
WHERE row_id = 1
UNION ALL
SELECT
cr.row_id,
cr.invoice_balance,
cr.invoice_id,
cr.total_amount,
CASE
WHEN cr.invoice_id = c.invoice_id THEN remaining_balance - cr.total_amount
ELSE remaining_balance
END,
CASE
WHEN cr.invoice_id = c.invoice_id THEN amount_paid + cr.total_amount
ELSE amount_paid
END
FROM
CTE c, CTE_R cr
WHERE c.row_id = cr.row_id -1
)
SELECT * FROM CTE
At this point I am stumped, because the remaining balance will go negative and not move to the next invoice that has a balance. Am I going about this the right way?
Edit: The other problem I am having is that the recursive CTE is very inefficient, and the query takes far too long.