Workbook for Volume 1 – Part IV - Section #5: Foundational Papers of the 19th Century & Before – Bernoulli (2 of 5)
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For returning readers and subscribers: This post introduces a Revised Version for Volume 1 – Part IV - Section #5: Foundational Papers of the 19th Century & Before – Bernoulli (2 of 5)
Summary:
Volume 1 – Part IV - Section #5: Foundational Papers of the 19th Century & Before – Bernoulli (2 of 5) - This section shows how Daniel Bernoulli developed the first “Repair Program” for the use of quantitative, decision-making tools from the Logic & Statistics Program, such as Expected Value”, when playing games of chance. This “Repair Program”, the “Expected Utility of Wealth”, comes from 18th Century observations that players of games of chance made choices in the context of their different initial levels of wealth. Bernoulli’s “Expected Utility” remained unchallenged as a best practice in Financial Economics from its first publication in 1738, up to the first two decades of the 21st Century. In 2018 a paper by Ole Peters & Alex Adamou, and titled “The time interpretation of expected utility theory” extended the findings of Peters’ 2011 paper about the St. Petersburg Paradox. This paper showed that utility functions do not need to come from explanations based on moral or irrational psychological re-weightings of monetary accounts that are external to the quantitative growth model. Peters & Adamou showed that similar functions develop from consistent, non-linear transformations that are internal to the model. In Peters’ work, and unlike Bernoulli’s work, arbitrary utility functions based on moral or psychological considerations are replaced with internally consistent mathematical functions based on the physical truth of time irreversibility for their respective “Growth Dynamics”. A specific “Growth Dynamic equation” implies a specific “Ergodic Transformation Function” (i.e. utility function), and vice-versa. This means that Peters’ work provides a generalized framework where Bernoulli’s logarithmic “Expected Utility of Wealth” becomes a special case that applies to a wealth process driven by a “Multiplicative Growth Dynamic”, and opens the door for material improvements in the accuracy of “Predictions” used for individual, investment decision-making.
Developing…
”CTRI by Francois Gadenne” writes a business book in three volumes, published serially on Substack for public peer-review. 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, & continuously updated with insights from reading Wealth, Health, & Statistics research papers on behalf of large companies as the co-founder of CTRI.