I love the psychological thriller genre, but I've always wondered what actually defines it. Two definitions come to mind: 1. A thriller that focuses on the psychological dimensions of the characters 2. A thriller in which the protagonist/s and antagonist/s engage in a battle not just on a physical level, but on a mental one as well. Some psycho-thrillers mix in elements from different genres, or otherwise subvert/avoid our expectations. Alfred Hitchcock's Psycho counts not only as a thriller, but as a slasher film, as do many works by Dario Argento. Marathon Man takes the story of a haunted grad student running from his past and applies it to a high-tension story of espionage and diamonds. The 2010 Edge of Darkness film does a similar thing, juxtaposing the conspiracy mystery with Mel Gibson's grief. Fight Club can be described as a psychological thriller, but the "thriller" part doesn't come until the last half-hour or so. If anything, its more of a dark dramedy. Psychological elements even pop up in different genres: the action/crime thriller Heat gives us a lot of insight into the characters of Al Pacino and Robert De Niro. In To Live and Die in L.A., a LOT of time is spent elaborating on how disturbingly similar William Petersen and Willem Defoe are, to the point that it could be considered a study of two self-destructive individuals.
your 2 definitions are pretty much on target... you can get more detailed answers to your question by simply googling 'define psychological thriller'...
I am going to shift the idea a little for you here. I too really enjoy a good psychological thriller - damned if I'd want to try and write one because I'm my own worst critic! A psychological thriller, regardless of the content, engages the psychological dimensions of the 'reader' in my opinion. It should ask questions of my psychological comfort zone - American Psycho for instance. Am I engaged in a psychologically 'creeped out' but still morbidly fascinated way.