papers/lux-smart-order-routing/sections/08-order-matching-priority.tex

\section{Order Matching Priority}
\label{sec:priority}

\subsection{Priority Rules}

The SOR applies the following priority hierarchy for venue selection:

\begin{enumerate}[nosep]
  \item \textbf{Price improvement}: Venues offering better prices are preferred.
  \item \textbf{Internalization}: If the Lux ATS internal book can fill the order at NBBO or better, the order is internalized (matched against resting orders on the internal book).
  \item \textbf{Settlement speed}: On-chain venues (T+0) are preferred over traditional venues (T+1) at equal price.
  \item \textbf{Fill rate}: Venues with higher expected fill rates are preferred.
  \item \textbf{Latency}: Among equal-quality venues, lower-latency venues are preferred.
  \item \textbf{Cost}: Trading fees are factored into the effective price.
\end{enumerate}

\subsection{Internalization Policy}

Internalization (matching orders against the internal book rather than routing to external venues) is permitted when:

\begin{itemize}[nosep]
  \item The internal book offers price improvement over the best external quote.
  \item The order can be fully filled from the internal book.
  \item Both parties pass compliance checks for the security \cite{lux-security-token-standard}.
\end{itemize}

When internalization provides no price improvement, orders are routed to the venue with the best composite score per the optimization in Section~\ref{sec:model}.