Convex Order and Arbitrage

Battle Count: 69

Directly relevant to quantitative trading through: (1) model-independent arbitrage detection via convex order testing, (2) construction of calendar spread strategies from recovered convex functions, (3) robust option pricing and hedging without model assumptions, (4) relative arbitrage between functionally generated portfolios. The paper provides both theoretical foundations and numerical algorithms for practical implementation. However, it lacks empirical validation with real market data and the conjecture linking convex order to portfolio arbitrage remains unproven.

Moderate to high complexity: requires knowledge of optimal transport theory (Kantorovich duality, Brenier's theorem), Bayesian optimization (TPE), convex analysis, PDE solving (Poisson equation with Neumann BCs), and stochastic calculus (semimartingales, gamma processes). Implementation uses multiple Python packages (POT, HyperOpt, cvxpy, scipy, dolfin). The non-convexity of the main optimization problem and the need for numerical recovery of convex functions in multiple dimensions add practical difficulty. The 2D recovery requires solving PDEs on irregular domains.

The paper references a GitHub repository for numerical implementation. Algorithms are clearly specified with pseudo-code (Algorithms 1-8). Uses standard Python packages (POT, HyperOpt, cvxpy, scipy, dolfin, matplotlib). Experiments use well-defined synthetic distributions (Gaussian, discrete). However, some hyperparameter choices and exact experimental settings are not fully detailed in the text.