Rewards

Method Summary
The rewards methodology is in part inspired by AIP-16. Rewards are allocated pro-rata across the markets based on the weighted dollar value of the TVL in the underlying market. Consider the following market:
Market
Supply
Borrow
Price [$]
TVL Weight
ALGO
600mm
50mm
1.80
1
goBTC
2k
1k
61000
2
goETH
10k
2k
4200
2
The ALGO, goBTC, and goETH weighted dollarized TVL are (600+50) * 1.8 * 1 = 1170mm, (0.002 + 0.001) * 61000 * 2 = 366mm, and (0.01 + 0.002) * 4200 * 2 = 100.8mm, respectively. The total weighted dollarized TVL is 1170 + 366 + 100.8 = 1636.8mm.
For example, if the protocol were issuing 100,000 ALGO tokens in rewards, then it would allocate 1170 / 1636.8 ~ 71% (71480 ALGOs), 366/1636.8 ~ 23% (22360 ALGOs), and 100.8/1636.8 ~ 6% (6160 ALGOs) of the rewards to the ALGO, goBTC, and goETH markets, respectively.
Then, within a given market, the protocol distributes the tokens on a pro-rata basis according to user supply TVL + borrow TVL. For example, within the ALGO market, the 71,480 tokens would be distributed evenly among the 600 + 50 = 650mm, resulting in ~109 ALGO tokens per 1mm of TVL.
Rewards Calculation
To calculate rewards for a given market, a cumulative sum construction is used where every time the manager contract updates, the amount of rewards paid out / market TVL is saved down. This quantity is the market rewards coefficient:
​
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where rewards paid to market m at time t is  
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where
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 is rewards paid per second to the protocol
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 is the time in seconds since the last manager update
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 is the dollarized weighted TVL for market m at time t where a given market's TVL is scaled by its weight parameter 
 : 
​
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 is the token TVL for market m at time t, the sum of the supply and borrow TVLs
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To calculate the rewards accrued by a supplier or borrower of K tokens in market m between times t1 and t2, the difference between the two cumsum coefficients is calculated and scaled by the user's TVL:
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Method Summary

Rewards Calculation