This was my brief for my last assignment. There've been plenty of (some dodgy) answers given since the start of textual criticism. Mostly because they decided that most psalms were written post-exile. Here's the last paragraph of the essay. (Full essay available to masochists via email upon request)
How shall we then read?
The strength of the argument for a representative king shows us that not all parts of all psalms can be directly appropriated by Christians, but in the light of the Christ’s reign. The strength of the ‘everyman’ argument is not found in its power to explain the origin of the psalms, but to describe their function. The individual laments came to be collected and used centrally partly because of their empathetic value. That many of them came from David in no way lessens their value for the everyman. In fact, for those who hold David dearly, it increases it. Individual laments are not open windows into that great man’s life, but portraits and self-portraits of it that the everyman can gaze at. Depending on the portrait he might see Christ, himself or both, and be instructed.Hmm.... perhaps posting excerpts from assignments isn't the best idea after all. That didn't really make sense, did it?
Who do YOU think the righteous sufferer is?