Fellow at the London Mathematical Laboratory
Friday 24th Oct, 15:30-17:00
INET Oxford Meeting Room (ground floor) INET Oxford
Eagle House, Walton Well Road, OX2 6ED
The classic decision-theory problem of evaluating gambles is treated from a modern perspective using dynamics. Gambles are random variables that model possible changes in monetary wealth. In the classic evaluation, money is transformed non-linearly into utility using a utility function, and the value of the gamble is defined as the expectation value of utility changes. Utility functions aim to capture individual psychological characteristics, but their generality limits predictive power. The expectation value defines the concept of rationality in economics: he who optimizes expectation values is rational. This notion of rationality is problematic because expectation values are only meaningful in the presence of ensembles or in ergodic systems, whereas decision-makers have no access to ensembles and no growth process representing wealth can be ergodic. Simultaneously addressing the shortcomings of utility and those of expectations, I propose to evaluate gambles by averaging wealth growth over time. No utility function is needed, but a dynamic must be specified to compute time averages. Linear and logarithmic “utility functions” appear not as representations of individual risk preferences but as transformations that generate ergodic observables for purely additive and purely multiplicative dynamics, respectively.