Thursday, 22 November 2012, 6:00PM
Barnard's Inn Hall

Time for a Change: Introducing irreversible time in economics

Dr Ole Peters

An exploration of the remarkable consequences of using Boltzmann's 1870s probability theory and cutting-edge 20th Century mathematics in economic settings. An understanding of risk, market stability and economic inequality emerges.

The lecture presents two problems from economics: the leverage problem "by how much should an investment be leveraged", and the St Petersburg paradox. Neither can be solved with the concepts of randomness prevalent in economics today. However, owing to 20th-century developments in mathematics these problems have complete formal solutions that agree with our intuition. The theme of risk will feature prominently, presented as a consequence of irreversible time.

Our conceptual understanding of randomness underwent a silent revolution in the late 19th century. Prior to this, formal treatments of randomness consisted of counting favourable instances in a suitable set of possibilities. But the development of statistical mechanics, beginning in the 1850s, forced a refinement of our concepts. Crucially, it was recognised that whether possibilities exist is often irrelevant -- only what really materialises matters. This finds expression in a different role of time: different states of the universe can really be sampled over time, and not just as a set of hypothetical possibilities. We are then faced with the ergodicity problem: is an average taken over time in a single system identical to an average over a suitable set of hypothetical possibilities? For systems in equilibrium the answer is generally yes, for non-equilibrium systems no. Economic systems are usually not well described as equilibrium systems, and the novel techniques are appropriate. However, having used probabilistic descriptions since the 1650s economics retains its original concepts of randomness to the present day.

The solution of the leverage problem is well known to professional gamblers, under the name of the Kelly criterion, famously used by Ed Thorp to solve blackjack. The solution can be phrased in many different ways, in gambling typically in the language of information theory. Peters pointed out that this is an application of the ergodicity problem and has to do with our notion of time. This conceptual insight changes the appearance of Kelly's work, Thorp's work and that of many others. Their work - fiercely rejected by leading economists in the 1960s and 1970s - is not an oddity of a specific case of an unsolvable problem solved. Instead, it is a reflection of a deeply meaningful conceptual shift that allows the solution of a host of other problems.

183

dr-ole-peters

Santa Fe Institute and the London Mathematical Laboratory (www.lml.org.uk).

Read More
Read Less

Transcript

22 November 2012

Time for a Change: Introducing irreversible time in economics
Dr Ole Peters

View PDF
Print
Related Future Lectures
Related Past Lectures
WATCHED

What is the Value of Finance and Insurance to the Economy?

Professor John Kay CBE FBA FRSE
Wednesday, 6 July 2016 - 6:30PM
WATCHED
Part of a series

Recession and Recovery

Professor Jagjit Chadha
Thursday, 29 September 2016 - 6:00PM
WATCHED
Part of a series

What have Mathematicians Done for Us?

Professor Chris Budd OBE
Tuesday, 11 October 2016 - 1:00PM
WATCHED
Part of a series

Curves in Honour of Leibniz's Tercentenary

Professor Jan van Maanen
Thursday, 27 October 2016 - 4:00PM
WATCHED

Leonardo, Rapunzel and the Mathematics of Hair

Professor Raymond E. Goldstein
Wednesday, 9 November 2016 - 6:00PM
WATCHED
Part of a series

The Challenge of Big Data

Professor Chris Budd OBE
Tuesday, 15 November 2016 - 1:00PM
WATCHED
Part of a series

Assessing the Economic Risks from Brexit

Professor Jagjit Chadha
Thursday, 2 June 2016 - 6:00PM
WATCHED
Part of a series

Mathematics, Measurement and Money

Professor Norman Biggs
Tuesday, 24 May 2016 - 6:00PM
WATCHED
Part of a series

The Efficient Markets Hypothesis

Professor Jagjit Chadha
Thursday, 28 April 2016 - 6:00PM
WATCHED
Part of a series

Turing and von Neumann

Professor Raymond Flood
Tuesday, 19 April 2016 - 1:00PM
WATCHED
Part of a series

Computers, People and the Real World

Professor Martyn Thomas CBE
Tuesday, 5 April 2016 - 6:00PM
WATCHED
Part of a series

Why Doesn't Capital Flow From High To Low?

Professor Jagjit Chadha
Thursday, 17 March 2016 - 6:00PM
WATCHED

Immigrants and the Economy: Positive Impact and Political Disregard

Professor Jagjit Chadha
Thursday, 2 June 2016 - 6:00PM
WATCHED

Information Cascade: How We Choose...

Professor Jagjit Chadha
Thursday, 28 April 2016 - 6:05PM
WATCHED

The Enigma Machine: How it Works

Professor Raymond Flood
Tuesday, 19 April 2016 - 1:10PM
WATCHED

The Fly Puzzle and Von Neumann's Response

Professor Raymond Flood
Tuesday, 19 April 2016 - 1:05PM
WATCHED
Part of a series

Success Story: Implementing the UK Air Traffic Control System

Professor Martyn Thomas CBE
Tuesday, 5 April 2016 - 6:20PM
WATCHED
Part of a series

Automation: Can You and Should You?

Professor Martyn Thomas CBE
Tuesday, 5 April 2016 - 6:15PM