Market viability and martingale measures under partial information

TL;DR

This paper investigates the conditions under which a financial market with partial information remains viable, establishing a link between utility maximization solutions and the existence of specific martingale measures.

Contribution

It provides a novel equivalence between market viability and the existence of partial information equivalent martingale measures, using maximum principles in stochastic control.

Findings

Market viability is characterized by the existence of partial information equivalent martingale measures.

Optimal portfolio problems are solvable up to a stopping time under partial information.

The paper offers a constructive proof approach and illustrates results with an example.

Abstract

We consider a financial market model with a single risky asset whose price process evolves according to a general jump-diffusion with locally bounded coefficients and where market participants have only access to a partial information flow. For any utility function, we prove that the partial information financial market is locally viable, in the sense that the optimal portfolio problem has a solution up to a stopping time, if and only if the (normalised) marginal utility of the terminal wealth generates a partial information equivalent martingale measure (PIEMM). This equivalence result is proved in a constructive way by relying on maximum principles for stochastic control problems under partial information. We then characterize a global notion of market viability in terms of partial information local martingale deflators (PILMDs). We illustrate our results by means of a simple example.