to mitigate the impact of excessive compounding and enhance long-term sustainability.
Adaptive rate limiters have been put in place to limit the effect of hyper-compounding and improve sustainability.
There are 5 tiers of Rate Limiters and your tier is determined by comparing the amount of rewards you have compounded vs your fresh USDC deposits.
You can calculate this with the following formula:
Define the Compound Reward Function (C(n)) and the New Deposit Function (D(m)), where (n) and (m) represent the number of days. For a given time period (t), the total compounded rewards and deposits can be expressed as follows:
$$ Ctotal(t)=\sum_{i=1}^{t} C(i), Dtotal(t)=\sum_{j=1}^{t} D(j) $$
The degree of Adaptive-Rate-Limiters (L) can be defined using the following conditional function:
Where (x) is the value of the Rate Limiter, determined by the difference between compounded rewards and new deposits:
$$ x=Ctotal(t)−Dtotal(t) $$
The daily earnings (E) on any given day (k) can be expressed as the current balance (B(k)) multiplied by the corresponding rate (L(x)):
$$ E(k)=B(k)⋅L(x) $$
The update of the balance (B) can be represented by a recursive function, where (B(0)) is the initial balance:
$$ B(k+1)=B(k)+E(k) $$
This recursive relationship can be used to calculate the balance for any future day, based on the balance from the previous day and the earnings received on that day. We can represent the continuous growth of future balances using the Laplace transform of L:
$$ {L}\{ B(t) \} = \mathcal{L}\{ B(0) \} + \mathcal{L}\{ \sum_{k=0}^{t-1} E(k) $$
The limiters are: