Ross Recovery with Recurrent and Transient Processes

TL;DR

This paper investigates the conditions under which the objective measure can be recovered from the risk-neutral measure in continuous-time models, especially focusing on transient processes where previous models failed.

Contribution

It extends Ross recovery theory to transient processes in continuous-time models, identifying the additional information needed for recovery.

Findings

Recovery is possible if the process is recurrent under the objective measure.

When the process is transient, additional information is required for recovery.

The paper clarifies the limitations of existing models in the transient case.

Abstract

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.