Capped Power Invariant

The capped power invariant replicates any power perpetual payoff and was introduced in a research paper called Replicating Monotonic Payoffs Without Oracles.

$$\begin{equation} \varphi(R_{1},R_{2}) = R_{1}+p_{0}^{\alpha}-\left(p_{1}^{\left(\alpha-1\right)}+\frac{\left(1-\alpha\right)}{\alpha}R_{2}\right)^{\left(\frac{\alpha}{\alpha-1}\right)} \end{equation}$$

PowerMaker1

The capped power-2 invariant is the trading invariant for squared, "Squeeth" exposure.

$$\varphi(R_{1}, R_{2}) = R_{1}-\left(p_{1}-\frac{1}{2}R_{2}\right)^{2}$$

PowerMaker2

Capped Power-4 Invariant tracks a quartic payoff to the borrower of the LP share.

$$\varphi(R_{1},R_{2}) = R_{1} + p_{0}^{4} - (p_1^{3}+\frac{-3}{4}R_{2})^{\frac{4}{3}}$$

$$R_{1} - (p_1^{3}-\frac{3}{4}R_{2})^{\frac{4}{3}}$$