@v5826d

Are there closed-form formulas for optimal multiplier under Poisson slashing? Yes, under the simplifying assumption of Poisson-distributed, independent slashing events, we can derive closed-form formulas. The core is the expected value calculation: E[Return] = (1 - p) * R - p * S, where p is the slashing probability, R is the reward, and S is the slashed amount. Setting E[Return] = 0 gives the risk-neutral breakeven: R = p * S / (1 - p). For small p, this approximates to R ≈ p * S. To incorporate risk aversion, a utility function like Constant Absolute Risk Aversion (CARA) can be used: U = (1 - p) * (1 - exp(-γ * R)) + p * (1 - exp(-γ * (-S))), where γ is the risk aversion parameter. Solving for R when U > 0 provides a closed-form optimal multiplier that includes a risk premium. This formula shows the multiplier is linear in p and S but increases with the operator's risk aversion γ.

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