Final answer:
Open Account would be the financing method used in this scenario.
Step-by-step explanation:
An exporter that enjoys good trustworthy relations with a buyer in a well-established market would likely use the financing method of Open Account.
Open Account is a method in which the exporter extends credit to the buyer and allows them to pay at a later date, typically after the goods have been delivered. This method is suitable when both parties have established trust and the buyer has a good payment history.
In this scenario, the exporter would not necessarily require any additional security measures such as a Letter of Credit or Cash in Advance. Documentary Collection may still be used, but Open Account is the most appropriate option given the established relationship and market conditions.