Precificação de opções financeiras: um estudo sobre os modelos de Black Scholes e Garch

Precificação de opções financeiras: um estudo sobre os modelos de Black Scholes e Garc

An upper limit to the secular variation of the gravitational constant from white dwarf stars

A variation of the gravitational constant over cosmological ages modifies the main sequence lifetimes and white dwarf cooling ages. Using an state-of-the-art stellar evolutionary code we compute the effects of a secularly varying G on the main sequence ages and, employing white dwarf cooling ages computed taking into account the effects of a running G, we place constraints on the rate of variation of Newton's constant. This is done using the white dwarf luminosity function and the distance of the well studied open Galactic cluster NGC 6791. We derive an upper bound G'/G ~ -1.8 10^{-12} 1/yr. This upper limit for the secular variation of the gravitational constant compares favorably with those obtained using other stellar evolutionary properties, and can be easily improved if deep images of the cluster allow to obtain an improved white dwarf luminosity function.Comment: 15 pages, 4 figures, accepted for publication in JCA

An independent constraint on the secular rate of variation of the gravitational constant from pulsating white dwarfs

A secular variation of the gravitational constant modifies the structure and evolutionary time scales of white dwarfs. Using an state-of-the-art stellar evolutionary code and an up-to-date pulsational code we compute the effects of a secularly varying $G$ on the pulsational properties of variable white dwarfs. Comparing the the theoretical results obtained taking into account the effects of a running $G$ with the observed periods and measured rates of change of the periods of two well studied pulsating white dwarfs, G117--B15A and R548, we place constraints on the rate of variation of Newton's constant. We derive an upper bound $\dot G/G\sim -1.8\times 10^{-10}$ yr$^{-1}$ using the variable white dwarf G117--B15A, and $\dot G/G\sim -1.3\times 10^{-10}$ yr$^{-1}$ using R548. Although these upper limits are currently less restrictive than those obtained using other techniques, they can be improved in a future measuring the rate of change of the period of massive white dwarfs.Comment: 13 pages, 4 tables, 3 figures. To be published in the Journal of Cosmology and Astroparticle Physic

Axions and White Dwarfs

White dwarfs are almost completely degenerate objects that cannot obtain energy from the thermonuclear sources and their evolution is just a gravothermal process of cooling. The simplicity of these objects, the fact that the physical inputs necessary to understand them are well identified, although not always well understood, and the impressive observational background about white dwarfs make them the most well studied Galactic population. These characteristics allow to use them as laboratories to test new ideas of physics. In this contribution we discuss the robustness of the method and its application to the axion case.Comment: 4 pages, 1 figure, to appear in the Proceedings for the 6th Patras meeting on Axions, WIMPs and WISP

Monte Carlo simulations of the halo white dwarf population

The interpretation of microlensing results towards the Large Magellanic Cloud (LMC) still remains controversial. Whereas white dwarfs have been proposed to explain these results and, hence, to contribute significantly to the mass budget of our Galaxy, there are as well several constraints on the role played by white dwarfs. In this paper we analyze self-consistently and simultaneously four different results, namely, the local halo white dwarf luminosity function, the microlensing results reported by the MACHO team towards the LMC, the results of Hubble Deep Field (HDF) and the results of the EROS experiment, for several initial mass functions and halo ages. We find that the proposed log-normal initial mass functions do not contribute to solve the problem posed by the observed microlensing events and, moreover, they overproduce white dwarfs when compared to the results of the HDF and of the EROS survey. We also find that the contribution of hydrogen-rich white dwarfs to the dynamical mass of the halo of the Galaxy cannot be more than $\sim 4$.Comment: 17 pages, 10 figures; accepted for publication in Astronomy and Astrophysic