2,883 research outputs found
In Defence of No Best World
Recent work in the philosophy of religion has resurrected Leibniz’s idea that there is a best possible world, perhaps ours. In particular, Klaas Kraay’s [2010] construction of a theistic multiverse and Nevin Climenhaga’s [2018] argument from infinite value theory are novel defenses of a best possible world. I do not think that there is a best world, and show how both Kraay and Climenhaga may be resisted. First, I argue that Kraay’s construction of a theistic multiverse can be resisted from plausible assumptions about set theory. Next, I argue against the value-theoretic assumptions that underlie Climenhaga’s argument and show how to give an infinite value theory where there is no best world
Surreal Decisions
Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our theory to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives
Performance analysis and optimal selection of large mean-variance portfolios under estimation risk
We study the consistency of sample mean-variance portfolios of arbitrarily
high dimension that are based on Bayesian or shrinkage estimation of the input
parameters as well as weighted sampling. In an asymptotic setting where the
number of assets remains comparable in magnitude to the sample size, we provide
a characterization of the estimation risk by providing deterministic
equivalents of the portfolio out-of-sample performance in terms of the
underlying investment scenario. The previous estimates represent a means of
quantifying the amount of risk underestimation and return overestimation of
improved portfolio constructions beyond standard ones. Well-known for the
latter, if not corrected, these deviations lead to inaccurate and overly
optimistic Sharpe-based investment decisions. Our results are based on recent
contributions in the field of random matrix theory. Along with the asymptotic
analysis, the analytical framework allows us to find bias corrections improving
on the achieved out-of-sample performance of typical portfolio constructions.
Some numerical simulations validate our theoretical findings
Fermion Pairing and the Scalar Boson of the 2D Conformal Anomaly
We analyze the phenomenon of fermion pairing into an effective boson
associated with anomalies and the anomalous commutators of currents bilinear in
the fermion fields. In two spacetime dimensions the chiral bosonization of the
Schwinger model is determined by the axial current anomaly of massless Dirac
fermions. A similar bosonized description applies to the 2D conformal trace
anomaly of the fermion stress tensor. For both the chiral and conformal
anomalies, correlation functions involving anomalous currents, or
of massless fermions exhibit a massless boson pole, and
the associated spectral functions obey a UV finite sum rule, becoming
-functions in the massless limit. In both cases the corresponding
effective action of the anomaly is non-local, but may be expressed in a local
form by the introduction of a new bosonic field, which becomes a bona fide
propagating quantum field in its own right. In both cases this is expressed in
Fock space by the anomalous Schwinger commutators of currents becoming the
canonical commutation relations of the corresponding boson. The boson has a
Fock space operator realization as a coherent superposition of massless fermion
pairs, which saturates the intermediate state sums in quantum correlation
functions of fermion currents. The Casimir energy of fermions on a finite
spatial interval can also be described as a coherent scalar
condensation of pairs, and the one-loop correlation function of any number
of fermion stress tensors may be expressed as a
combinatoric sum of linear tree diagrams of the scalar boson.Comment: 58 pages, 8 figures; v2: minor revision, to appear in JHE
El Crèdit a llarg termini a Barcelona a la segona meitat del segle XIV: els censals morts i els violaris
El Crèdit a llarg termini a Barcelona a la segona meitat del segle XIV: els censals morts i els violaris
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