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In Both Cases, Who Is the Party That Assumes the Risk?

In both cases, the party receiving the payment assumes the risk. The options seller (writer) receives the premium and assumes the price risk of the underlying asset moving unfavorably.

The mining pool operator receives the fee and assumes the variance risk (the luck of finding a block) inherent in the Proof-of-Work process, especially under a Pay-Per-Share (PPS) scheme. The payment is the compensation for taking on this specific financial risk.

How Does the PPS Payout Scheme Transfer Risk from Miners to the Pool Operator?
Can a Mining Pool Be Considered a Form of ‘Risk-Sharing’ Financial Arrangement?
How Does the Severity of the Penalty Differ between CEX and DEX Manipulation Cases?
How Does a Mining Pool Divide the Work of Finding a Valid Nonce?