I'm glad things worked out better for you when you confronted your pursuer. When there's something bad happening in my dreams it never gets better. If they catch me, it's all over, fear intensity goes critical and I wake up breathing heavy.
Coincidentally the Page-A-Day Dream Calendar from the 10th talked about knives:
A knife is a threat, no doubt about it. It cuts food, objects, even human beings. However, in your dreams, even when blood is spouting and someone is hurt, the knife is only slicing through a psychic barrier. If youíre being chased by a knife-wielding menaceóa common nightmareóyou are running from a part of yourself that wants blood contact. Any aspects of yourself to which youíve closed your heart can be pretty relentless in dreams. "