Technology Category
Game Theory and Economic Paradigms: EquilibriumReasoning under Uncertainty: Stochastic OptimizationMultiagent Systems: Mechanism Design
Radner equilibrium with population growth
🤖 AI Summary
This paper investigates the existence of Radner equilibria in a dynamic general equilibrium framework with uninsurable income and unbounded population growth, and analyzes their implications for perpetual annuity pricing. We develop a Poisson-based demographic model integrating lifecycle consumption and annuity investment decisions, and employ stochastic equilibrium modeling, exponential utility optimization, truncation-limit arguments, and numerical simulation. First, we establish—rigorously and for the first time—the existence of Radner equilibria in infinite-population economies. Second, we demonstrate that higher birth rates significantly dampen annuity price volatility. Third, we identify that intergenerational heterogeneity in discount rates—particularly stronger present bias among younger agents—systematically elevates equilibrium annuity prices. These findings extend the theoretical foundations of asset pricing and demographic economics in incomplete markets, bridging population structure dynamics with equilibrium asset valuation under uninsurable labor income risk.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Existence of Radner equilibrium with population growth
Impact of birth rate on annuity price oscillations
Effect of age-based time preference on annuity prices
Innovation
Methods, ideas, or system contributions that make the work stand out.
Proves Radner equilibrium with population growth
Uses Poisson rate for agent population growth
Analyzes annuity price effects from birth rates
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