Lecture notes

The notes below are our attempt to re-develop economic theory from scratch, namely starting with the axiom that individuals optimize what happens to them over time, not what happens to them on average in a collection of parallel worlds. The latter, surprisingly, is the starting point of the currently dominant form of economic theory.

The new formalism is being developed at the London Mathematical Laboratory. The lectures were first presented at a winter school on complex systems in Chandigarh, India, as part of a collaboration between the Indian Institute of Science and Educational Research Mohali and the Santa Fe Institute. The lectures were given to a group of about 50 students and have since then been downloaded thousands of times. We intend to publish them as a book when they have fully matured.

Date Size PDF Comment
2018-06-30 6.6MB (136 pages) Download Ch.1: discussion of random variable, stochastic processes, ergodicity.
Ch.2: general mapping dynamics utility function (beyond Kelly, includes historical example of square-root Cramer utility).
Ch.3: log-normals vs. power laws, sums of log-normals, random-energy model.
Ch.4: New chapter. Re-allocating Geometric Brownian Motion (RGBM). Analytic solution of RGBM. Analysis of US wealth data.
Ch.5: Applications of stochastic market efficiency: solution of the equity premium puzzle, central-bank interest rate setting, fraud detection, a theory of noise. New data analysis, including tests of predictions for SP500 total return, DAX, bitcoin, Bernie Madoff’s Ponzi scheme.
2017-08-24 4.5MB (96 pages) Download Corrected bullet point 4, p.26.
2017-07-12 4.5MB (96 pages) Download Harmonised notation.
2017-04-18 4.5MB (96 pages) Download Fixed some references and typos.
2017-03-04 4.5MB (96 pages) Download

7 thoughts on “Lecture notes

  1. Hi, is knowledge of elementary calculus-based probability (as in Bertsekas and Tsitsiklis, or the elementary Ross book) sufficient to grasp the notes?

    Liked by 1 person

  2. Francis, thank you for your question, that’s very helpful. Next time we go through the notes we will make a list of any prerequisites.
    We’re trying to keep the lecture notes fairly self-contained, and I will cautiously say yes, the books you mention should be sufficient. My sense is that too much prior knowledge is more likely to be problematic than too little. But please let us know how you’re getting on, especially if you get stuck somewhere and feel that something is missing.


  3. Hello, I am working through these lecture notes and love them. I do not come from a math or physics background and I find this to be a great resource for understanding your published papers. I have a pedantic comment to make: in eq (13) you introduce tau as a ‘dummy variable indicating a specific round of a gamble’ but it is not noted upon until eq (30). Trivial, but it would be easier to understand if noted in the text when it is first introduced.


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