The time resolution of the St Petersburg paradox

@article{Peters2011TheTR,
  title={The time resolution of the St Petersburg paradox},
  author={Ole Peters},
  journal={Philosophical transactions. Series A, Mathematical, physical, and engineering sciences},
  year={2011},
  volume={369},
  pages={4913 - 4931}
}
  • O. Peters
  • Published 19 November 2010
  • Economics
  • Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
A resolution of the St Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is derived using a conceptually different argument. The advantage of the time resolution is the elimination of arbitrary utility functions. 

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References

SHOWING 1-10 OF 57 REFERENCES

Time and risk

Intertemporal choice has obvious similarities with choice under uncertainty. However, because of technical difficulties in mapping results between the two domains, theoretical analysis of these

The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern

From insurance rates, to housing and job markets, to the safety of cars and planes, calculating probabilities allowed people, for the first time, to think rationally about how future events might unfold.

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

An Estimate of the Degrees of the Mortality of Mankind

In his Use 5 Halley refers to “years purchase”, the price charged for an annuity paying one dollar per year. Parliament granted William and Mary permission in 1691 to borrow money through an annuity

The Conceptual Foundations of the Statistical Approach in Mechanics

By Paul and Tatiana Ehrenfest, translated by Michael J. Moravcsik Ithaca: Cornell University Press; London: Oxford University Press. Pp. xvi + 114. Price 24s. This little book is a long overdue

Proof of the Quasi-Ergodic Hypothesis.

  • J. Neumann
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1932
The quasi-ergodic hypothesis of classical Hamiltonian dynamics is generalized with the aid of the reduction of Hamiltonian systems to Hilbert space, and with the use of certain methods of the authors' closely connected with recent investigations of the algebra of linear transformations in this space.

A new interpretation of information rate

The maximum exponential rate of growth of the gambler's capital is equal to the rate of transmission of information over the channel, generalized to include the case of arbitrary odds.

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

PROOFS AND REFUTATIONS (I)*†

  • I. Lakatos
  • Mathematics
    The British Journal for the Philosophy of Science
  • 1963
Introduction § 1. A Problem and a Conjecture. §2. A Proof. § 3. Criticism of the Proof by Counterexamples which are Local but not Global. § 4. Criticism of the Conjecture by Global Counterexamples.
...