Ole Peters, London Mathematical Laboratory, London, UK
Supposedly, science and mathematics are of limited use in economics because of the human element, because the system responds to attempts of modelling it, because the effort is self-referential. My experience of difficulties in economics is different. Failing to replicate foundational results in the field, I have found that a number of problems are unresolved because economics got the mathematics wrong. In seminal papers from the 1700s to the 2000s basic mathematical errors have been propagated. The errors invalidate fundamental theorems.
Starting with the simple observation that no stochastic growth process is ergodic, I show a sequence of "big results" in economics that are undermined and topple in domino-like fashion. Part of this can be understood historically. Leading economists explicitly restricted formal economics to ergodic equilibrium models; since such models bear no resemblance to the actual economy, non-ergodic far-from equilibrium models are used in practice (the random walk was invented here). The result is conceptually self-contradictory and mathematically flawed.
In the seminar I will resolve the leverage problem and the St Petersburg paradox. I will show that Bernoulli (1738) made a small error that was corrected by Laplace (1814). The error was re-introduced by Menger (1934) and incorporated in v. Neumann and Morgenstern's (1944) axiomatic formulation of utility theory. From there it propagated to decision theory, game theory and thereby all major branches of economics. I will list further questions that we have addressed. I conclude that economics is hard, but less hard once basic mathematical errors are corrected.