when there’s (implicit) measure+when there is none

Needs a Measure – r or mu. Whenever we see “drift”, it means expected growth or the Mean of some distribution (of a N@T). There’s a probability measure in the context. This could be a physical measure or a T-fwd measure or a stock-numeraire or the “risk-neutral-measure” i.e. MoneyMarketAcct as the numeraire

Needs a Measure – dW. Brownian motion is always a probabilistic notion, under some measure

Needs a Measure – E[…] is expectation of something. There’s a measure in the context.

Needs a Measure – Pr[..]

Needs a Measure – martingale

Regardless of measure – time-zero fair price of any contract. The same price should result from derivation under any measure.

Regardless of measure – arbitrage is arbitrage under any measure

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