Long-Run Heterogeneity in an Exchange Economy with Fixed-Mix Traders

Abstract

We consider an exchange economy with heterogeneous agents and multiple assets and investigate the coupled dynamics of assets’ prices and agents’ wealth. We assume that agents have heterogeneous beliefs and invest on each asset a fraction of wealth proportional to its expected dividends. Our main finding is that long-run coexistence of heterogeneous agents is a generic outcome of the market dynamics. We provide sufficient conditions for the latter, as well as sufficient conditions for the relative wealth of any given agent converging to zero or to one. Since we use a direct approach that combines the inter-temporal dynamics of wealth and prices via agents’ portfolio rules, we can characterize when long-run heterogeneity occurs for both complete and incomplete asset markets.

Keywords: Market Selection Hypothesis; Heterogeneous Beliefs; Evolutionary Finance; Incomplete Markets; Asset Pricing; Generalized Kelly rule.

JEL Classification: C60, D52, D53, G11, G12