by Hideki Takayasu, Kiyoshi Kanazawa, Misako Takayasu
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Suggested foundations for probability and statistical reasoning and stochastic processes and pricing. Specialist prerequisites vary by paper.
Read the distributions and expectations used in probabilistic arguments.
Understand what it means to condition on current information.
Follow Brownian dynamics and the second-order term in Itô calculus.
Assess uncertainty rather than treating an estimate as a fact.
Connect stochastic dynamics to no-arbitrage prices.
Translate continuous dynamics into a numerical experiment.
Move from conditioning and expected values to timed problems with a defensible solution.
Start in discrete time, move to Brownian motion, then read the original pricing argument and simulate it.