The continuous behavior of the numeraire portfolio under small changes in information structure, probabilistic views and investment constraints

TL;DR

This paper investigates how the numeraire portfolio's behavior remains stable under small, continuous changes in market information, probabilistic models, and investment constraints, providing insights into its robustness in dynamic financial environments.

Contribution

It establishes the continuous dependence of the numeraire portfolio on market parameters, highlighting its stability under infinitesimal changes in information, probability measures, and constraints.

Findings

Numeraire portfolio exhibits stable behavior under small parameter changes.

Theoretical framework for continuous dependence in continuous-path markets.

Insights into robustness of optimal investment strategies.

Abstract

The numeraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes, when deflated by it, supermartingales. The numeraire portfolio depends on market characteristics, which include: (a) the information flow available to acting agents, given by a filtration; (b) the statistical evolution of the asset prices and, more generally, the states of nature, given by a probability measure; and (c) possible restrictions that acting agents might be facing on available investment strategies, modeled by a constraints set. In a financial market with continuous-path asset prices, we establish the stable behavior of the numeraire portfolio when each of the aforementioned market parameters is changed in an infinitesimal way.