Luminescent solar concentrators (LSCs) are designed to guide sunlight to a small photovoltaic solar cell. Thus far, light propagation in LSCs has been modeled using heuristic / statistical approaches. We propose a deterministic theory for this problem based on radiative transfer. This model take into account accurately the multiple absorption and reemission of light at different wavelengths. The performance of LSCs based on semiconductor nanoparticles is studied in detail by computing solutions of this model. The results are compared with Monte Carlo simulations of photon transport. These results suggest that optimized LSCs could offer a more affordable route to photovoltaic technology.