Cross-border payment networks are best understood not as static pipelines, but as dynamic, non-stationary graphs in which each routing decision reshapes the system itself - shifting liquidity, altering token prices, and changing the future feasibility and cost of available paths. Traditional routing and max-flow algorithms fail in this setting because they assume fixed capacities and independent edges, while real-world markets exhibit flow-dependent costs, endogenous feedback loops, and rapidly evolving state.

This work reframes cross-border FX and stablecoin-based settlement as a real-time control problem under uncertainty, where optimal decisions must account for both current conditions and the impact of execution on future network states. The approach integrates short-horizon forecasting with stochastic optimization to enable adaptive routing across chains, tokens, venues, and time in a continuously changing environment.