Ross Recovery with Recurrent and Transient Processes

Recently, Ross showed that it is possible to recover an objective measure from a risk-neutral measure. His model assumes that there is a finite-state Markov process X that drives the economy in discrete time. Many authors extended his model to a continuous-time setting with a Markov diffusion process X with state space R. Unfortunately, the continuous-time model fails to recover an objective measure from a risk-neutral measure. We determine under which information recovery is possible in the continuous-time model. It was proven that if X is recurrent under the objective measure, then recovery is possible. In this article, when X is transient under the objective measure, we investigate what information is sufficient to recover.