Evaluating gambles using dynamics.

@article{Peters2016EvaluatingGU,
  title={Evaluating gambles using dynamics.},
  author={Ole Peters and Murray Gell-Mann},
  journal={Chaos},
  year={2016},
  volume={26 2},
  pages={
          023103
        }
}
Gambles are random variables that model possible changes in wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes. Utility functions aim to capture individual psychological characteristics, but their generality limits predictive power. Expectation value maximizers are defined as rational in economics, but expectation values are only meaningful in the presence of ensembles or in… 

Figures from this paper

Ergodicity-breaking reveals time optimal decision making in humans
TLDR
It is suggested that the findings of this work motivate a need for explicitly grounding theories of decision-making on ergodic considerations, and show that utility functions are modulated by gamble dynamics in ways not explained by prevailing decision theories.
Ergodicity-Breaking Reveals Time Optimal Economic Behavior in Humans
Ergodicity describes an equivalence between the expectation value and the time average of observables. Applied to human behaviour, ergodic theory reveals how individuals should tolerate risk in
Fitness-maximizers employ pessimistic probability weighting for decisions under risk
TLDR
An evolutionary principal–agent model is developed in which individuals utilize a set of proximal choice variables to account for the non-linear dependence of these variables on consumption, and maximum fitness can be achieved by adopting pessimistic probability weightings compatible with the rank-dependent expected utility family of choice models.
Hierarchical Evolutionary Preferences Explain Discrepancies in Expected Utility Theory
TLDR
An evolutionary principal-agent model is developed in which individuals maximize a set of proximal choice variables, the interests of which are aligned with fitness, and it is shown that age-specific demographic rates can be used as choice variables.
Rational insurance with linear utility and perfect information
We present a mathematical solution to the insurance puzzle. Our solution only uses time-average growth rates and makes no reference to risk preferences. The insurance puzzle is this: according to the
Discounting Desirable Gambles
TLDR
This paper considers two routes to relaxing the commitment to linearity of the desirable gambles framework and the machinery for coherent inference, including a method for describing rewards called discounted utility.
The ergodicity problem in economics
The ergodic hypothesis is a key analytical device of equilibrium statistical mechanics. It underlies the assumption that the time average and the expectation value of an observable are the same.
On the statistical differences between binary forecasts and real-world payoffs
  • N. Taleb
  • Economics
    International Journal of Forecasting
  • 2020
The Impact of Time Horizon on the Effect of Diversification
Although investors are often advised to diversify their investment portfolios as well as to consider rebalancing them periodically, research has shown that they often ignore this advice. We try to
...
...

References

SHOWING 1-10 OF 40 REFERENCES
The Use of Unbounded Utility Functions in Expected-Utility Maximization: Comment
The standard solution to the problem of rational decision making under uncertainty is to postulate the existence of a von Neumann-Morgenstern-type utility function, the expected value of which the
Optimal leverage from non-ergodicity
In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another
Colloquium: Statistical mechanics of money, wealth, and income
This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution
The evolutionary advantage of cooperation
TLDR
This analysis rests on the insight that evolutionary processes are typically multiplicative and noisy and makes it a candidate explanation of cooperation in settings too simple for other fitness gains, such as emergent function and specialization, to be probable.
Asset Pricing
TLDR
This report focuses specifically on quantitative structural asset pricing models, and some of these models provided an important base for understanding financial institutions, frictions in financial markets, liquidity, investor heterogeneity, and the potential presence of investor irrationality in some markets.
Theory of Games and Economic Behavior.
This is the classic work upon which modern-day game theory is based. What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together
Random multiplicative processes: An elementary tutorial
An elementary discussion of the statistical properties of the product of N independent random variables is given. The motivation is to emphasize the essential differences between the asymptotic N→∞
Decoherent Histories Quantum Mechanics with One 'Real' Fine-Grained History
Decoherent histories quantum theory is reformulated with the assumption that there is one “real” fine-grained history, specified in a preferred complete set of sum-over-histories variables. This real
Exposition of a New Theory on the Measurement of Risk
EVER SINCE mathematicians first began to study the measurement of risk there has been general agreement on the following proposition: Expected values are computed by multiplying each possible gain by
Ergodicity breaking in geometric Brownian motion.
TLDR
The effects of diversification using the concept of ergodicity breaking is studied, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time average.
...
...