papers/lux-omnichain-yield/sections/09-performance-fee-mechanics.tex

\section{Performance Fee Mechanics}
\label{sec:fees}
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\subsection{Fee Structure}

Two fees apply to yield-bearing bridge tokens:

\begin{enumerate}[nosep]
  \item \textbf{Bridge fee} ($f_b$, default 10 bps, max 100 bps): Charged on deposit/withdrawal. Applied to the principal.
  \item \textbf{Performance fee} ($f_y$, default 1000 bps = 10\%): Charged on yield only. Never on principal.
\end{enumerate}

The yield distributed to share holders after fees:

\begin{equation}\label{eq:net_yield}
  Y_{\text{net}}(t) = Y_{\text{gross}}(t) \cdot \left(1 - \frac{f_y}{10{,}000}\right)
\end{equation}

Performance fees are distributed according to the stakeholder share:

\begin{equation}\label{eq:fee_split}
  \text{toStakeholders} = Y_{\text{gross}} \cdot \frac{f_y}{10{,}000} \cdot \frac{f_s}{10{,}000}
\end{equation}

where $f_s$ is the stakeholder share (default 9000 bps = 90\%). The remaining 10\% goes to the protocol treasury.

\subsection{Fee Accounting in Share Price}

Performance fees are extracted by minting additional shares to the fee recipient rather than reducing the backing:

\begin{equation}\label{eq:fee_shares}
  \Delta S_{\text{fee}} = \frac{Y_{\text{gross}} \cdot f_y / 10{,}000}{p(t)}
\end{equation}

This dilution-based approach ensures the share price never decreases due to fee extraction---it simply grows slower than the gross yield rate. The share price after fee extraction:

\begin{equation}
  p'(t) = \frac{B(t) + Y_{\text{gross}}}{S(t) + \Delta S_{\text{fee}}} = \frac{B(t) + Y_{\text{gross}}}{S(t) + \frac{Y_{\text{gross}} \cdot f_y / 10{,}000}{p(t)}}
\end{equation}

Since $f_y / 10{,}000 < 1$, we have $p'(t) > p(t)$ whenever $Y_{\text{gross}} > 0$, preserving the monotonicity property of Theorem~\ref{thm:monotone}.

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