Convergence of the financial value of weak information for a sequence of discrete-time markets

TL;DR

This paper investigates the value of weak anticipations in discrete and continuous-time financial markets, establishing convergence of their financial value in complete markets, thereby linking discrete models to continuous ones.

Contribution

It introduces a minimal probability measure for weak anticipations and proves the convergence of their financial value from discrete to continuous-time markets in complete settings.

Findings

Weak anticipations are characterized by a minimal probability measure.

Financial value of weak information converges from discrete to continuous markets.

Results apply specifically to complete market models.

Abstract

We examine weak anticipations in discrete-time and continuous-time financial markets consisting of one risk-free asset and multiple risky assets, defining a minimal probability measure associated with the anticipation that does not depend on the choice of a utility function. We then define the financial value of weak information in the discrete-time economies and show that these values converge to the financial value of weak information in the continuous-time economy in the case of a complete market.