Notation

This page summarizes the notation used in the subsequent sections.

$\nu_{ij}$: the position of the$j\text{-th}$account in the$i\text{-th}$asset

$a_i$: the amount of the$i\text{-th}$asset owner by the protocol

$c_i$: the contribution of the$i\text{-th}$asset into the capital, denominated in the$i\text{-th}$asset

$C$: the capital value denominated in the base currency

$p_i$: the current price of the $i\text{-th}$ asset denominated in the base currency

$r_i$: the current borrow rate for the$i\text{-th}$asset

$V^+_i$: the sum of all the positive (long) positions in the$i\text{-th}$asset

$V^-_i$: the sum of all the negative (short) positions in the$i\text{-th}$asset

$\phi_r$: the interest rate fee

$\rho_i$: the current effective deposit rate for the$i\text{-th}$asset

$\phi_d$: the deposit fee

$\phi_w$: the withdrawal fee

$\phi_s$: the sell fee

$\phi_b$: the buy fee

$m_i$: the margin quotient for the$i\text{-th}$asset

$\mu_j$: the marginal value of the$j\text{-th}$account

$\nu_j$: the net value of the$j\text{-th}$account

$\lambda$: the liquidator's reward

$\nu^+_j$: the sum of the values of all the positive (long) positions of the$j\text{-th}$account denominated in the base currency

$\nu^-_j$: the sum of the values of all the negative (short) positions of the$j\text{-th}$account denominated in the base currency

$\alpha$: the capitalization ratio

$N$: the total number of protocol tokens in circulation

$p$: the current spot price of a protocol token

$N_0$: the initial number of protocol tokens

$C_0$: the initial value of the capital

$p_0$: the initial price of a protocol token

$\phi_m$: the minting fee

$\phi_b$: the burning fee

$\sigma_i$: the share of the$i\text{-th}$in the capital

$\tau_i$: the target capital allocation for the$i\text{-th}$asset

$\rho$: the capital rebalance reward

$C^+$: the sum of all the capital assets

$C^-$: the negative sum of all the capital obligations