Just thought I'd mention that there are banks in Robert Jordan's Wheel of Time books. Off the top of my head I think there's a modest section of New Spring (the novel) that deals with letters of credit and such.
I've said before that with enough ranks in Forgery and enough cajones you can practically write your own money. But then, that's only if you have institutions in your game world that work with things like letters of credit, a letter of rights, or borrowing against your property or family name (if you're a noble).
What happens to you when the king finds out someone is stealing money from him through forged letters of credit is another story...
Forging a deed to "your enormous tracts of land" and then borrowing large sums of money using the land as collateral seems safer.
Think about this; in a world where a guy with a sword can go out, kill the beast, and literally come home a few days later with a lifetime's (for a commoner anyway) worth of wealth, why wouldn't someone offer to fund him.
If your PC comes back from slaying the dragon or what have you and dumps his money in the bank, that bank will prosper. After you've proven you aren't just getting lucky, the bank might even let you borrow against your reputation as a competent monster-hunter so you can buy better equipment. They fund your venture for a cut of the treasure and the right to house your cut in their banks. They might keep equipment on hand to lend to you if it becomes common practice.
Sure, you might die in some far away dungeon and the bank will lose the +3 flaming sword they loaned you, but is it any riskier than some of the financial gambles certain institutions make these days?
That's not even touching the idea of private investors funding you, but that's a bit too far off-topic.