In many ways I think the conflict of the story is resolved sufficiently. Santiago's struggle is as much with himself as it is with the fish. His essential question is whether or not he is still physically and mentally capable of catching large fish at his age. His experiences answer that question. Although he may not have been successful in bringing the fish back to shore, he has proven to himself that he can do it.
The portion of the conflict that is perhaps left unresolved (and I think this gets to the heart of your question) involves the notoriety and recognition Santiago fails to receive from his community regarding his abilities as a fisherman. Again, I'm not sure this is of primary importance to Santiago, but one way for this to be resolved is to imagine how the boy lives his life differently because of this experience. Perhaps he is the one who champions Santiago's abilities and re-tells Santiago's story. Or perhaps the boy becomes an expert fisherman himself and then credits all of his knowledge back to Santiago. Either way, Santiago's talent would live on and he would receive the recognition to which some feel he may be entitled.
I took your question to mean how I would have solved it if I were the author. I have to admit that while I was reading it, I hoped that the old man would be able to bring in some of this great fish and be able to gain the respect of the community and perhaps even show the young man that he was strong and could still fish with the best of them.
But as I think about it, this conflict is such a real one, where in the end there isn't really a clear winner and loser, perhaps just two losers. We so often divide things up and assume there is a winner and a loser (for example in wars) but generally there are only losers and this story does a great job of demonstrating that idea.