Who's the author of the following short story? It's a famous writer from the 50/60s.
A clerk is in love with a female colleague who ignores him. When his mother dies, he picks up sailing. A storm makes him shipwrecked on a deserted island. One day another castaway arrives, the woman he loved, who went searching for him. They have a brief happy period, then begin to fight until he kills her. However she was a hallucination. He is rescued and confesses the murder. The woman, who was at home and never went searching for him, reads the news in the newspapers.