A price that reverts to θ = $1.00, with a typical swing σ/√(2κ) of 10¢ and a half-life ln 2/κ; money is worth r = 5% a year; one unit is held at a time. One round trip (Leung and Li, 2015): sell when the price reaches b₁, buy when it falls to d₁. Repeated trading (Zervos, Johnson and Alazemi, 2013): the value of being flat, J, and of being long, V, each include the other, and the two levels d and b come from four conditions of value matching and smooth fit.
Published: both problems and the form of their solutions. Ours: the solver, every number on this page (15 half-lives × 6 costs, each checked against a finite-difference solution that uses none of the formulas) and the waiting times, from the process's speed measure.