Relative Arbitrage Problem Under Eigenvalue Lower Bounds

Battle Count: 93

The paper provides deep theoretical foundations for understanding when and how relative arbitrage (beating the market) is possible under volatility constraints. While not directly implementable as a trading algorithm, it characterizes critical time horizons T* beyond which arbitrage exists in sufficiently volatile markets. The eigenvalue-based volatility condition connects to practical factor models used in empirical finance. The results inform the design of portfolio strategies in stochastic portfolio theory and provide rigorous bounds on when market-beating strategies can exist. However, the paper is highly theoretical and does not provide practical trading signals or implementable strategies directly.

This is a pure mathematics paper requiring advanced knowledge of: (1) stochastic analysis and semimartingale theory, (2) viscosity solution theory for fully nonlinear PDEs, (3) geometric measure theory and mean curvature flows, (4) stochastic optimal control and dynamic programming, (5) spectral theory of matrices, and (6) functional analysis. There is no computational implementation described. The theoretical framework involves proving existence, uniqueness, and regularity of solutions to complex nonlinear PDEs on general compact domains.

This is a purely theoretical mathematics paper with no computational experiments, code, or empirical data. Reproducibility is limited to verifying the mathematical proofs. The paper builds on prior work by Larsson and Ruf [LR21, LR24] and extends their framework. No numerical implementations or datasets are provided.