10 research outputs found
Rough paths in idealized financial markets
This paper considers possible price paths of a financial security in an
idealized market. Its main result is that the variation index of typical price
paths is at most 2, in this sense, typical price paths are not rougher than
typical paths of Brownian motion. We do not make any stochastic assumptions and
only assume that the price path is positive and right-continuous. The
qualification "typical" means that there is a trading strategy (constructed
explicitly in the proof) that risks only one monetary unit but brings infinite
capital when the variation index of the realized price path exceeds 2. The
paper also reviews some known results for continuous price paths and lists
several open problems.Comment: 21 pages, this version adds (in Appendix C) a reference to new
results in the foundations of game-theoretic probability based on Hardin and
Taylor's work on hat puzzle
Higgs field in cosmology
The accelerated expansion of the early universe is an integral part of modern
cosmology and dynamically realized by the mechanism of inflation. The simplest
theoretical description of the inflationary paradigm is based on the assumption
of an additional propagating scalar degree of freedom which drives inflation -
the inflaton. In most models of inflation the fundamental nature of the
inflaton remains unexplained. In the model of Higgs inflation, the inflaton is
identified with the Standard Model Higgs boson and connects cosmology with
elementary particle physics. A characteristic feature of this model is a
non-minimal coupling of the Higgs boson to gravity. I review and discuss
several phenomenological and fundamental aspects of this model, including the
impact of quantum corrections and the renormalization group, the derivation of
initial conditions for Higgs inflation in a quantum cosmological framework and
the classical and quantum equivalence of different field parametrizations.Comment: 36 pages, 9 figures; references added, typos corrected. Invited
contribution to the Heraeus-Seminar "Hundred Years of Gauge Theory", 30 July
- 3 August 2018, Physikzentrum Bad Honnef, organized by Silvia De Bianchi and
Claus Kiefer. To appear in the proceedings "100 Years of Gauge Theory. Past,
present and future perspectives" in the series `Fundamental Theories of
Physics' (Springer
A new class of nearly self-financing strategies
For a large class of models, we prove that the stop-loss start-gain trading strategy is as close to producing arbitrage as we please. (C) 2002 Elsevier Science B.V. All rights reserved