ADR: Revise interest curve utilization rate definition

[jordanschalm]

No description provided.

[zhangchiqing]

Why B depositing 105 units would make totalDebit(X) to 0? Could you add more details in the comments.

[jordanschalm]

Because they are unsigned and clamp to zero. From the paragraph above:

They are stored as absolute (not interest-adjusted) unsigned values, which can cause updates to the values to clamp to zero

Also added a ceil function in the equation to represent the "unsigned-ness"

[zhangchiqing]

I'm still confused by this example. What does this "10% debit rate and 1 year passes" change? I thought after 1 year pass, User B would need to pay 110 units of X, then after B deposits 105 units of X, the totalDebit(X) would be 110 - 105 = 5, instead of ceil(100 - 105, 0) = 0. Did I miss anything?

[jordanschalm]

• When User B withdraws 100X, totalDebit(X) is set to 100
• After a year passes with 10% interest rate:
  • User B owes 110 units of X
  • But totalDebit(X) is still 100 - the value only changes on deposits and withdrawals, and does not account for interest, as it is currently implemented.

[zhangchiqing]

It seems there is a cycle dependency:

1. the calculation of utilization needs the totalTrueCreditBalance and totalTrueDebitBalance
2. the calculation of totalTrueCreditBalance needs interest
3. the calculation of interest needs utilization. (cycle?)

[jordanschalm]

The interest and utilization are inter-related, but I think in practice that is OK. We apply each change in sequence, modifying one at a time:

1. Something mutates (wlog) totalTrueCreditBalance(X), eg. addToCreditBalance(trueCreditValue)

• totalTrueCreditBalance is stored as a scaled value
• we compute scaledCreditValue based on interestIndex(X)
• at this point, interestIndex(X) is the index before the addToCreditBalance(trueCreditValue) operation occurs
• we set totalScaledCreditBalance = totalScaledCreditBalance + scaledCreditValue

2. The next time we do something that requires an interest rate, we re-compute the interest index based on the latest state.

• we compute utilization rate based on totalTrueCreditBalance, as modified in step 1

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Abstractly, for discrete time steps t:

• totalTrueCreditBalance[t] = someFunction(totalTrueCreditBalance[t-1], interestIndex[t-1])
• interestIndex[t] = someOtherFunction(totalTrueCreditBalance[t-1], interestIndex[t-1])

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Besides being convenient (and possible to compute), I think this is also the most conceptually correct way to calculate these values.

• Interest accumulates over time
• I make a (wlog) deposit at time t, the last update was at time t-1, and the next update is at time t+1
• The update at time t should include interest accumulated between t-1 and t
• The interest A accumulated between t-1 and t occurs before my deposit at time t -- my deposit shouldn't affect A, because it happened after A was accumulated
• The interest B accumulated between t and t+1 occurs after my deposit at time t -- my deposit should affect B, because it happened before B was accumulated