Existence and convergence of discrete-time Kyle models with multiple insiders

Battle Count: 68

This paper provides foundational theoretical results for market microstructure models with multiple partially informed traders. While not directly implementable as a trading strategy, it resolves long-standing open problems that underpin the theoretical framework used in algorithmic trading, market making, and price impact modeling. The Kyle model and its extensions are central to understanding how informed trading affects prices, which is critical for execution algorithms and market design.

This is a pure mathematical theory paper with no computational implementation. The proofs involve advanced techniques including polynomial root analysis, shooting methods for nonlinear difference equations, Kalman filtering, ODE theory, and multi-step induction arguments. The mathematical sophistication is very high, requiring expertise in stochastic processes, game theory, and real analysis. There is no code or algorithm to implement directly.

The paper is entirely self-contained with complete mathematical proofs. All definitions, theorems, lemmas, and proofs are provided in detail. No computational experiments or code are needed. However, the proofs are highly technical and require advanced mathematical maturity to verify. The parameter restrictions and model setup are fully specified.