Fees

Dynamic Liquidity Fee

$$\mathrm{fee}= \begin{cases} \dfrac{B}{R}, & \text{if improved,}\\ B\cdot R, & \text{otherwise.} \end{cases}$$

• Where R(N) is:

  $$R(N) = 1 + k\begin{cases} \dfrac{T-N}{T-m}, & \text{if } N \le T \text{ and } T\ne m,\\ \dfrac{N-T}{M-T}, & \text{if } N > T \text{ and } T\ne M,\\ 0, & \text{otherwise.} \end{cases}$$

• And:

  $$\text{improved} = \begin{cases} \lvert N - T\rvert < \lvert C - T\rvert, & \text{if } N \neq T,\\ C \neq T, & \text{if } N = T. \end{cases}$$

• Where:

  C is the current ratio.

  N is the new ratio.

  T is the target ratio.

  k is the multiplier.

  m is the lower fee band anchor ratio.

  M is the upper fee band anchor ratio.

  B is the base fee.

• Clarify:

  The lower and upper fee band anchor ratios shape the fee curve. They are not hard deposit or withdraw limits.

Fee Table

Action	Fee	Fee routing	Rent recipient
Add liquidity	Dynamic liquidity fee	25% company / 75% pool	None
Remove liquidity	Dynamic liquidity fee	25% company / 75% pool	None