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.

The next version will be posted no later than 1 July 2018.

It will include

- In Chapter 2: the general mapping between dynamics and utility (currently only the special cases of additive and multiplicative dynamics are treated).
- In Chapter 3: the closed-form ergodic wealth distribution for reallocating GBM, where it exists (currently we compute only its moments); and the finite-time, finite-population asymptotics of sums of GBMs and their connection to the random energy model.
- In Chapter 4: an updated data analysis for stochastic market efficiency. Currently we use a data set that does not account for dividends, and this affects the results significantly.

Date | Size | Comment | |

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 |

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

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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.

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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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Hugh, many thanks! We’ve made a note and will correct this in the next update.

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