How well do you know your main charcter?
As the character is ficticious, you are the only one who can look deep inside her mind, but do you?
How do you describe the real character in a first person story? The character beneath the surface. Does she lie to the reader; does she lie to you? And can a real psychopath feel emotion?
Your character will (should, damn it, even though she is a psychopath) develop throughout the story. Her opinions will change, but will they change because "that is how it's supposed to be" or do things happen to her, things beyond your control, for we all know that once a story flows, it's hard to stop, and before you know it, your MC has a change of heart. Does that mean your MC was lying when she said she had no friends and no need for them, after which she avenges the death of the only person she had contact with. She says she is never angry and that she has never cried in her life, but when she hears of a child molester released on bail on suspicion of murder, her trigger-finger starts to itch and her eyes become moist.
I often ask myself if I am in control of my main character, or is she (in this case) in control of me. 
