Supplement Liquidity based modeling of asset price bubbles via random matching

TL;DR

This supplement provides proofs and properties related to a dynamical system model for asset price bubbles based on liquidity and random matching, complementing the main paper.

Contribution

It offers rigorous proofs and detailed properties of the dynamical system introduced in the original liquidity-based asset bubble model.

Findings

Proof of existence of the dynamical system D

Properties of the dynamical system D

Enhanced theoretical foundation for the model

Abstract

This is a supplement to the paper "Liquidity based modeling of asset price bubbles via random matching". The supplement is organized as follows. First, we prove Theorem 3.13 in [1] which provides the existence of the dynamical system D introduced in Definition 3.6 in [1]. Second, we show some properties of D which are summarized in Theorem 3.14 in [1]. In the following, we only state the basic setting and refer to [1] for definitions.