Book Editing: “Making Good Decisions” – Revised Part IV – Section #48:
“Calculated Projections” with the Tools of the 21st Century (Part 6 of 10) – From Normal to Log-Normal & Back
This free, public post shares the edited version of Part IV – Section #48
For readers that do not have the time to read the two-page pdf:
Part IV - Section #48:“Calculated Projections” with the Tools of the 21st Century (Part 6 of 10) – From Normal to Log-Normal & Back – This section presents a graphical illustration of the relationship between the exponential position equation [x = e^y] of the multiplicative “Growth Dynamic” [dx = x(μdt + σdW)], and its inverse, utility-like, ergodic transformation function, the logarithm function [y = ln x]. This example illustrates how Ergodicity Economics can derive specific “Growth Dynamics” from specific utility functions using the mathematics of invertible functions to develop the matching position equations. This means that utility functions from “Expected Utility Theory” other than the logarithm function, such as Modern Portfolio Theory’s implied quadratic utility function, have position equations other than the exponential function. Specific “Growth Dynamics”, and matching position equations need to be derived & paired with these utility functions in order to create consistent, apples-to-apples financial models.
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“CTRI by Francois Gadenne” writes a business book, published on Substack for public peer-review, at the rate of one two-page section per day. The book connects the dots of life-enhancing practices for the next generation, free of controlling algorithms, based on the lifetime experience of a retirement age entrepreneur, and continuously updated with insights from Wealth, Health, and Statistics research performed on behalf of large companies as the co-founder of CTRI.