Non-conservative optimal transport

Battle Count: 71

The paper provides a rigorous theoretical framework directly motivated by portfolio rebalancing with transaction costs. It establishes existence of optimal rebalancing trades and connects the problem to optimal transport theory. However, it is primarily a mathematical theory paper rather than a practical trading system. The framework could inform algorithmic execution strategies and portfolio management, but no computational methods or backtests are provided. The connection to entropic OT for tracking problems and the dynamic formulation for optimal execution are noted but not developed.

The theoretical framework requires deep knowledge of optimal transport theory, measure theory, convex analysis, and functional analysis. Implementing the non-conservative Kantorovich problem would require solving constrained optimization problems over spaces of measures. The dynamic formulation involves solving ODEs/PDEs with non-standard boundary conditions. The discrete version (portfolio rebalancing) is more tractable as a linear program, but the general continuous case is mathematically demanding.

The paper is purely theoretical with complete mathematical proofs provided in the main text and appendices. All definitions, theorems, and propositions are rigorously stated and proved. No computational experiments or numerical results are presented. The mathematical framework is fully self-contained with clear assumptions stated.