First, Mary Ann Tolbert contributes with "The Prodigal Son: An Essay in Literary Criticism from a Psychoanalytic Perspective" here's the abstract:
One of the major concerns of biblical interpretation is the need to relate ancient texts to contemporary situations. The tools and methodologies found in the field of literary criticism can aid immeasurably in this endeavor. As one possible example of such a study this essay explores the content of the parable of The Prodigal Son by the categories of a psychoanalytically oriented criticism and the form of the parable by a rhetorical analysis of its surface structure. Such a procedure emphasizes the unity of the narrative as a whole as well as the correspondences between thematic elements and their structural presentation. Elements of Freud’s mental typography, the id, the ego, and the superego, are shown to bear some striking similarities to the younger son, father, and elder son of the parable. In the central figure of the father, moreover, the basic human desire for reconciliation and restoration of unity, a theme developed by the parable as a whole, is symbolically expressed.
Next, Dan O. Via Jr. chimes in with "The Prodigal Son: A Jungian Reading."
An analysis (using Bremond’s model) is made of the narrative functions of the story showing that the prodigal son part and the elder brother part parallel each other in reverse order. Having demonstrated the narrative relationships within the story and allowing these to define the connections of the psychological categories, an intra-psychic interpretation is then given in the effort to show that the dynamics involved are the alienation of the ego from the Self and its reintegration through coming to terms with the shadow.
Finally, Bernard B. Scott contributes with "The Prodigal Son: A Structuralist Interpretation"
The traditional interpretation of the parable of The Prodigal Son has been dominated by the identification of the elder son with the Pharisees. The first part of the paper seeks to show that this identification will not adequately interpret the parable. The second part of the paper undertakes an analysis of two of the parable’s intermediate structures: the narrative and mythical structures. This analysis points out that the elder son is not rejected in the parable, but serves to call into question the audience’s traditional mythical understanding of the relation between elder and younger sons.
I might have more to say on these after I read them more thoroughly, and reflect on whether or not I think they're out to lunch (a possibility I can't rule out yet).