papers/lux-liquid-staking/sections/05-slashing-insurance.tex

\section{Slashing Insurance}
\label{sec:insurance}

\subsection{Insurance Pool Mechanics}

The insurance pool absorbs slashing losses before they affect sLUX holders:

\begin{algorithm}[H]
\caption{Slashing Loss Absorption}
\label{alg:insurance}
\begin{algorithmic}[1]
\Procedure{HandleSlashing}{validator $v_i$, slashAmount}
    \State $\mathsf{insBalance} \gets$ InsurancePool.balance()
    \If{$\mathsf{slashAmount} \leq \mathsf{insBalance}$}
        \State InsurancePool pays $\mathsf{slashAmount}$ \Comment{Fully covered}
        \State sLUX holders unaffected
    \Else
        \State InsurancePool pays $\mathsf{insBalance}$
        \State $\mathsf{shortfall} \gets \mathsf{slashAmount} - \mathsf{insBalance}$
        \State $\mathsf{totalPooled} \gets \mathsf{totalPooled} - \mathsf{shortfall}$ \Comment{Socialized loss}
        \State sLUX exchange rate decreases by $\mathsf{shortfall}/\mathsf{totalPooled}$
    \EndIf
    \State Remove $v_i$ from active validator set
\EndProcedure
\end{algorithmic}
\end{algorithm}

\subsection{Insurance Pool Sizing}

\begin{proposition}[Insurance Adequacy]
With a 5\% reward fee funding the insurance pool and a maximum single-validator slashing rate of 5\% (equivocation), the insurance pool covers a single slashing event after:
\begin{equation}
    T_{\text{cover}} = \frac{0.05 \cdot \delta_{\max}}{0.05 \cdot y \cdot P} = \frac{\delta_{\max}}{y \cdot P}
\end{equation}
epochs, where $\delta_{\max}$ is the maximum delegation to one validator, $y$ is the per-epoch yield, and $P$ is the total pool.
\end{proposition}

With $\delta_{\max} = 0.10P$, $y = 0.02\%$ per epoch: $T_{\text{cover}} = 0.10P / (0.0002 \cdot P) = 500$ epochs $\approx 1.4$ years. After this period, the insurance pool can fully absorb a single-validator equivocation event.

\subsection{Insurance Pool Lower Bound}

\begin{definition}[Target Insurance Ratio]
The target insurance ratio is:
\begin{equation}
    \mathsf{targetIR} = \frac{\mathsf{InsurancePool.balance}}{\mathsf{totalPooled}} \geq 0.02 \quad (2\%)
\end{equation}
When the ratio exceeds 5\%, excess funds flow to the treasury rather than the insurance pool.
\end{definition}