ETD

• ABM
• asset pricing model
• equilibrium market curve
• evolutionary finance
• heterogeneous agents
• incomplete markets
• investment strategies
• Kelly criterion
• market selection
• portfolio choices
• price feedbacks
• stability analysis
• steady-state simulation analysis
• wealth dynamics

This thesis studies what becomes of the Kelly criterion once it leaves the idealized world in which it was born and enters a strongly incomplete financial market. The economy considered here includes a risk-free asset, a single long-lived risky asset, and an infinite state space. In this setting, two competing generalizations of the Kelly principle are studied: the generalized Kelly rule of evolutionary finance, based on expected relative dividends, and an approximate log-optimal rule, derived from a local expansion of expected log-wealth and combined with adaptive learning.

Their interaction generates a system in which beliefs, portfolio choices, prices, returns, and wealth shares jointly evolve over time. To study this system, the thesis combines bifurcation analysis of the deterministic skeleton with statistically disciplined agent-based simulations of the stochastic model.

The results show that the two Kelly-inspired rules prevail under different conditions. The approximate log-optimal trader dominates when dividend yields are low and learning is cautious, whereas the generalized Kelly trader dominates when fundamentals are strong or volatility is high. Fast updating destabilizes the adaptive rule, while coexistence is generically not stable.

The broader implication is that, in incomplete markets, the Kelly criterion does not survive as a unique portfolio rule. It survives as a set of competing growth principles, whose success depends on the overall economic environment.