## Economics

**People**

LML Fellows **Ole Peters** (PI) @ole_b_peters, **Colm Connaughton** @CPCannaughton, **Oliver Hulme** @hulme_oliver, **Yonatan Berman** @bermanjoe and their collaborators contribute to LML’s economics programme. In addition to the theoretical work at LML, experiments are conducted at the Danish Research Center for Magnetic Resonance, supported by the Novo Nordisk Foundation.

**Summary**

The project is a re-write of economic theory, taking account of the ergodicity question: are averages over time identical to expectation values (averages across the stochastic ensemble)? This is effective because the foundations of economic theory were laid at a time when our formal understanding of randomness was in its infancy and conceptually immature. Yet the key formal models of human behavior used in economics are models of decision-making under randomness. These themes are explored through the **EE portal**.

Visit our channel at www.ergodicity.tv for introductory videos.

**Science-history background**

- Economics was the first discipline to develop the mathematics of randomness (17th century).
- The early conceptualisation of randomness has a flaw: it assumes that randomness playing out over time has the same effect as randomness playing out over an ensemble of parallel systems (parallel universes). In modern terms, it assumes ergodicity.
- Economics noticed symptoms that arise from this flaw and designed tools, most notably utility theory (18th century), that mitigate some of them.
- In the 19th century a new conceptualisation of randomness emerged in the context of physics, namely in thermodynamics and statistical mechanics. This conceptualisation recognises from the start the central role of time and makes the ergodicity problem explicit. It thereby resolves the fundamental flaw, rather than treating its symptoms.

** References**

[13] O. Peters

The ergodicity problem in economics.

Nature Phys. 15, 1216–1221 (2019).

doi:10.1038/s41567-019-0732-0

[12] O. Peters and A. Adamou

*The sum of log-normal variates in geometric Brownian motion.*

**arXiv:1802.02939** (2018).

[11] O. Peters and A. Adamou

*The time interpretation of expected utility theory.*

**arXiv:1801.03680** (2018).

[10] Y. Berman, O. Peters, and A. Adamou

*Far from equilibrium: Wealth reallocation in the United States.*

**arXiv:1605.05631** (2016).

[9] A. Adamou and O. Peters

*Dynamics of inequality.*

*Significance ***13**, 3, 32–37 (2016).

** doi:10.1111/j.1740-9713.2016.00918.x**

[8] O. Peters and M. Gell-Mann

*Evaluating gambles using dynamics.*

*Chaos ***26**, 023103 (2016).

** doi:10.1063/1.4940236**

[7] O. Peters and A. Adamou

*Rational insurance with linear utility and perfect information.*

**arXiv:1507.04655** (2015).

[6] O. Peters and A. Adamou

*The evolutionary advantage of cooperation.*

**arXiv:1506.03414** (2015).

[5] O. Peters and W. Klein

*Ergodicity*** b**reaking in geometric Brownian motion.

*Phys. Rev. Lett. *110, 100603 (2013).* *arXiv:1209.4517

**doi:10.1103/PhysRevLett.110.100603**

[4] O. Peters and A. Adamou

*Leverage Efficiency. *

*Santa Fe Institute Working Paper*#2013-06-022 (2013).

*arXiv:1101.4548*

[3] O. Peters

*Menger 1934 revisited.*

**arXiv:1110.1578 **(2011).

[2] O. Peters

*The time resolution of the St Petersburg paradox.*

*Phil. Trans. R. Soc. A* 369, 369, 1956, 4913–4931 (2011).

**arXiv:1011.4404**

**doi:10.1098/rsta.2011.0065**

[1] O. Peters

*Optimal leverage from non-ergodicity.*

*Quant. Fin.* **11**, 11, 1593–1602 (2011).

**doi:/10.1080/14697688.2010.513338**

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