Investing is Compression

Battle Count: 69

Highly relevant to quantitative trading. The paper provides a rigorous information-theoretic foundation for the Kelly criterion, proves its optimality, and offers practical tools: (1) the three-term decomposition clarifies what drives portfolio growth, (2) the backtesting insight that differences in log growth directly measure relative divergence in bits, (3) the winner fraction heuristic for VC-style allocation with a provable entropy bound. The work bridges information theory and portfolio management, offering new analytical tools for strategy comparison and capital allocation.

The theoretical framework is mathematically sophisticated (KL divergence, type classes, Stirling's approximation, convex optimization). However, the practical applications are relatively straightforward: the winner fraction heuristic requires only estimating per-asset win probabilities (not full joint distributions), and the backtesting comparison requires only computing differences in log growth rates. The main implementation challenge is estimating the true distribution or win probabilities in practice.

The paper is entirely theoretical with complete mathematical proofs (equations 1-69). All derivations are self-contained and verifiable. No empirical experiments or code are needed to validate the theoretical results. The winner fraction heuristic and entropy bound are stated as original contributions with full proofs provided.