The indifference value of the weak information

TL;DR

This paper introduces an indifference pricing framework to quantify the value of weak information in financial models, analyzing stability, invariance of claims, and differences between complete and incomplete markets.

Contribution

It develops a tractable indifference pricing method for weak information, establishes stability conditions, and characterizes information-invariant claims in various market settings.

Findings

Indifference prices quantify the value of weak information.

Stability conditions for indifference pricing are established with counterexamples.

In complete models, all contingent claims are invariant to weak information.

Abstract

We propose indifference pricing to estimate the value of the weak information. Our framework allows for tractability, quantifying the amount of additional information, and permits the description of the smallness and the stability with respect to small perturbations of the weak information. We provide sharp conditions for the stability with counterexamples. The results rely on a theorem of independent interest on the stability of the optimal investment problem with respect to small changes in the physical probability measure. We also investigate contingent claims that are indifference price invariant with respect to changes in weak information. We show that, in incomplete models, the class of information-invariant claims includes the replicable claims, and it can be strictly bigger. In particular, in complete models, all contingent claims are information invariant. We augment the results with examples and counterexamples.