Recently, Ross suggested 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. This article extends 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. Many authors have 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 necessary and sufficient to recover. We also introduce the notion of a reference function, which contains the information near the area where the process X lies with high probability under the objective measure. We discuss what type of condition for the reference function is necessary and sufficient for recovery .
Recently, Ross suggested 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. This article extends 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. Many authors have 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 necessary and sufficient to recover. We also introduce the notion of a reference function, which contains the information near the area where the process X lies with high probability under the objective measure. A reference function will be used for empirical purposes when X is transient under the objective measure .
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We discuss what type of condition for the reference function is necessary and sufficient for recovery
A reference function will be used for empirical purposes when X is transient under the objective measure