Long-run survival in limited stock market participation models with power utilities

Battle Count: 74

This is a foundational theoretical paper in mathematical finance. While it does not directly propose trading strategies or algorithms, it provides important insights into how market participation constraints and heterogeneous time preferences affect long-run equilibrium dynamics and trader survival. These insights are relevant for understanding market microstructure, the role of restricted investors, and the long-run behavior of asset prices in incomplete markets. The results on survival/extinction of traders have implications for understanding which market participants persist over time.

The paper requires advanced knowledge of stochastic analysis, ODE theory (particularly singular ODEs), diffusion process boundary classification, and general equilibrium theory. The mathematical machinery involves proving global existence of C1 solutions to non-linear singular path-dependent ODEs, applying comparison principles, Gronwall's inequality, and Feller's boundary classification. There is no computational implementation described; the contribution is purely analytical.

The paper is entirely theoretical with complete mathematical proofs. All derivations, lemmas, and theorems are self-contained with detailed proofs in Section 3. No computational experiments or datasets are involved. Reproducibility depends on the reader's ability to verify the mathematical arguments, particularly the ODE analysis and boundary classification of the one-dimensional diffusion.