by Ioannis Karatzas, Steven E. Shreve
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Suggested foundations for stochastic processes and pricing and probability and statistical reasoning. Specialist prerequisites vary by resource.
Interpret expectations after information is observed.
Follow Brownian dynamics and the second-order term in Itô calculus.
Read the distributions and expectations used in probabilistic arguments.
Connect stochastic dynamics to no-arbitrage prices.
Translate continuous dynamics into a numerical experiment.
Assess uncertainty rather than treating an estimate as a fact.
Start in discrete time, move to Brownian motion, then read the original pricing argument and simulate it.
Move from conditioning and expected values to timed problems with a defensible solution.