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.
In the book The Old Man and the Sea, Santiago struggles with the fish he has caught because he has to prove to himself that he is still a good fisherman. He is old and tired and has not caught a big fish in a long time. The younger boy looks up to him. I believe he also wants to show the boy that he is still worthy of his praise and admiration.
I believe that if I were like Santiago, I would have done the same thing. Sometimes we have to step out of our comfort zone to prove to ourselves that we can do something. I am a bicycle rider and I was asked to join a race. I never thought that I could do it, but I wanted to challenge myself. It was horrible. My legs ached after the first mile up hill. On the way down the hills I felt accomplished and thought that I was doing great. Then came four more really long stretches that were straight up hill and every time I saw a stop station I thought this is it I can't go on. Yet, even in tears I kept going. The ride was the longest ten miles of my life. I made it to the end and was one of the last groups in. I made it though and proved to myself that I could do it. To this day I feel really great about it, but I won't ever do it again!