## Economics

Mathematical treatments of randomness started with gambling problems and from there moved quickly to more general economic settings in the 17th century. Physics did not seriously consider randomness before the mid-19th century. However, when physicists entered the discussion with much more clearly defined problems, our understanding took a leap forward.

Mostly, this is the leap into ergodic theory and the recognition that the mathematics developed in the 17th and 18th century was only appropriate for the very special class of ergodic systems. Economics models — for instance any that exhibit growth — are usually not ergodic. Examples are the random walk or geometric Brownian motion. But economics stuck to its 17th-century methods rather than adopt new techniques in the 19th and 20th century. We apply the new techniques to old problems and find new answers. Some of these answers are of tremendous importance to the current state of economics and to many economic and political debates.

This work has attracted much interest from the investment community.

Literature

O. Peters and A. Adamou

*Stochastic Market Efficiency. *

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

www.santafe.edu/media/workingpapers/13-06-022.pdf

*arXiv:1101.4548*

www.santafe.edu/media/workingpapers/13-06-022.pdf

O. Peters

*Menger 1934 revisited.***arXiv:1110.1578**(2011).

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**

O. Peters

*Optimal leverage from non-ergodicity.**Quant. Fin.*

**11**, 11, 1593–1602 (2011).

**arXiv:0902.2965v2**

**doi:/10.1080/14697688.2010.513338**