To Bubble or Not to Bubble: Asset Price Dynamics and Optimality in OLG Economies

ArXiv ID: 2508.03230 “View on arXiv”

Authors: Stefano Bosi, Cuong Le Van, Ngoc-Sang Pham

Abstract

We study an overlapping generations (OLG) exchange economy with an asset that yields dividends. First, we derive general conditions, based on exogenous parameters, that give rise to three distinct scenarios: (1) only bubbleless equilibria exist, (2) a bubbleless equilibrium coexists with a continuum of bubbly equilibria, and (3) all equilibria are bubbly. Under stationary endowments and standard assumptions, we provide a complete characterization of the equilibrium set and the associated asset price dynamics. In this setting, a bubbly equilibrium exists if and only if the interest rate in the economy without the asset is strictly lower than the population growth rate and the sum of per capita dividends is finite. Second, we establish necessary and sufficient conditions for Pareto optimality. Finally, we investigate the relationship between asset price behaviors and the optimality of equilibria.

Keywords: Overlapping Generations (OLG), Asset Pricing, Bubbly Equilibria, Pareto Optimality, Dividend Models, Equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats
• Why: The paper is a theoretical macroeconomic model based on overlapping generations and dynamic systems with heavy use of advanced mathematics (optimization, existence proofs, dynamic equilibrium characterization), while it contains no data, backtesting, or implementation details, making it purely theoretical.

  flowchart TD
    A["Research Goal: Characterize asset price dynamics & Pareto optimality in OLG economies with bubbles"] --> B["Methodology: Analytical general equilibrium modeling"]
    B --> C["Key Inputs: Stationary endowments, standard assumptions, dividend structure"]
    C --> D["Computational Process: Derive equilibrium conditions & Pareto optimality criteria"]
    D --> E{"Scenario Analysis: Existence of bubbles?"}
    E --> F["Bubbleless Only"]
    E --> G["Bubbleless + Bubbly Continuum"]
    E --> H["All Equilibria Bubbly"]
    F & G & H --> I["Key Findings: Bubble existence if & only if interest rate < growth rate & dividends finite"]
    I --> J["Outcome: Complete characterization of price dynamics & Pareto optimal conditions"]