The Martin Integral Representation of Markovian Pricing Kernels

TL;DR

This paper uses the Martin integral representation to characterize all market beliefs consistent with a given risk-neutral measure in Markovian settings, with applications to long-term market behavior and recovery theorems.

Contribution

It introduces a comprehensive framework for understanding market beliefs via Martin representation, linking it to long-term dynamics and recovery results.

Findings

Provides a complete characterization of beliefs under Markovian models.

Connects Martin representation to long-term market behavior.

Discusses implications for the Ross recovery theorem.

Abstract

The purpose of this article is to describe all possible beliefs of market participants on objective measures under Markovian environments when a risk-neutral measure is given. To achieve this, we employ the Martin integral representation of Markovian pricing kernels. Then, we offer economic and financial implications of this representation. This representation is useful to analyze the long-term behavior of the state variable in the market. The Ross recovery theorem and the long-term behavior of cash flows are discussed as applications.