Paper: arXiv 2603.16108

Authors: Jaime Alberto Londoño

Abstract

We develop a continuous-time general equilibrium framework for economies with a heterogeneous population – modeled as a continuum – that repeatedly optimizes over short horizons under relative-income (Duesenberry-type) criteria. The cross-section evolves through a Brownian flow on a type space, transporting an effective impatience field that captures time variation in preferences induced by demographic changes, aging, and broader social shifts. We establish three main results. First, we prove an optimal consumption–investment theorem for infinite heterogeneous populations in this Brownian-flow setting. Second, we define a \emph{short-horizon Duesenberry equilibrium} – a sequential-trading (Radner-type) equilibrium in which agents repeatedly solve vanishing-horizon problems under a relative-income criterion – and provide a complete characterization and existence proof under mild regularity conditions; notably, market completeness and absence of (state-tame) arbitrage emerge endogenously from the market clearing, rather than being imposed as hypotheses. Third, we derive sharp asset-pricing implications: in equilibrium, the market price of risk is pinned down by the volatility of aggregate \emph{total wealth} (financial plus human capital), implying that the equity premium is governed by the magnitudes and correlations of wealth and equity volatilities rather than by consumption volatility alone. This shifts the equity premium puzzle from an implausibly low consumption volatility to a question about the volatility of aggregate total wealth. The framework delivers explicit decompositions of the risk-free rate that are consistent with macro-finance stylized facts. All equilibrium quantities are expressed in terms of market primitives.

Complexity vs Empirical Score

  • Math Complexity: 9.2/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly sophisticated continuous-time general equilibrium model using Brownian flows and infinite heterogeneous agents, yielding strong novel theoretical insights into the equity premium puzzle. However, it is purely theoretical with minimal empirical backtesting or real-world data validation provided in the summary.

Research Flowchart

  flowchart TD
    A[Research Goal: Explain Asset Pricing & Equity Premium via Short-Horizon Relative-Income Criteria] --> B[Input Primitives: Heterogeneous Population, Brownian Flow Type Space, Relative-Income Criteria]
    B --> C[Methodology: Continuous-Time General Equilibrium Framework]
    C --> D[Computational Step: Solve Short-Horizon Optimal Consumption-Investment Problem]
    D --> E[Computational Step: Derive Sequential-Trading Radner-Type Equilibrium]
    E --> F[Outcome 1: Endogenous Market Completeness & Absence of Arbitrage]
    E --> G[Outcome 2: Market Price of Risk Pinned to Volatility of Aggregate Total Wealth]
    E --> H[Outcome 3: Resolution of Equity Premium Puzzle & Risk-Free Rate Decompositions]