# Notation

$$\nu\_{ij}$$: 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