Paper: arXiv 2504.18009
Authors: Jin Hyuk Choi, Kim Weston
Abstract
We prove the existence of a Radner equilibrium in a model with population growth and analyze the effects on asset prices. A finite population of agents grows indefinitely at a Poisson rate, while receiving unspanned income and choosing between consumption and investing into an annuity with infinitely-lived exponential preferences. After establishing the existence of an equilibrium for a truncated number of agents, we prove that an equilibrium exists for the model with unlimited population growth. Our numerics show that increasing the birth rate reduces oscillations in the equilibrium annuity price, and when younger agents prioritize the present more than older agents, the equilibrium annuity price rises compared to a uniform demographic.
Complexity vs Empirical Score
- Math Complexity: 8.5/10
- Empirical Rigor: 2.0/10
- Quadrant: Lab Rats — theoretically deep, empirically untested
Why this score: The paper presents a rigorous theoretical breakthrough by establishing the existence of a continuous-time Radner equilibrium with unbounded Poisson population growth using infinite-dimensional recursive systems and Lambert W functions. However, as a purely mathematical finance study, it lacks empirical validation or backtesting on real-world demographic and asset pricing data.
Research Flowchart
flowchart TD
A[Research Goal: Prove Radner Equilibrium Existence & Asset Price Effects with Population Growth] --> B[Model Inputs: Poisson Birth Rate, Unspanned Income, Annuity Investment & Exponential Utility]
B --> C[Step 1: Truncate Model to a Finite Population of Agents]
C --> D[Step 2: Prove Equilibrium Existence for Truncated Model]
D --> E[Step 3: Extend Proof to Unlimited Population Growth]
E --> F[Numerical Analysis & Simulations]
F --> G[Key Outcomes: Higher Birth Rate Dampens Price Oscillations; Younger Present-Bias Increases Annuity Price]