This model replicates a number of the stochastic processes from Dixit & Pindyck’s Investment Under Uncertainty. It includes Brownian motion (Wiener process), geometric Brownian motion, mean-reverting and jump processes, plus forecast confidence bounds for some variations.
Units balance, but after updating this model I’ve decided that there may be a conceptual issue, related to the interpretation of units in parameters of the Brownian process variants. This arises due to the fact that the parameter sigma represents the standard deviation at unit time, and that some of the derivations gloss over units associated with substitutions of dz=epsilon*SQRT(dt). I don’t think these are of practical importance, but will revisit the question in the future. This is what happens when you let economists get hold of engineers’ math. 🙂
These structures would be handy if made into :MACRO:s for reuse.
stochastic processes 3.mdl (requires an advanced version of Vensim)
stochastic processes 3.vpm (published package; includes a sensitivity setup for varying NOISE SEED)
stochastic processes 3 PLE.mdl (Runs in PLE, omits only one equation of low importance)