Minimization of the root of a quadratic functional under a system of affine equality constraints with application in portfolio management

AbstractWe present an explicit closed form solution of the problem of minimizing the root of a quadratic functional subject to a system of affine constraints. The result generalizes Z. Landsman, Minimization of the root of a quadratic functional under an affine equality constraint, J. Comput. Appl. Math. 2007, to appear, see 〈http://www.sciencedirect.com/science/journal/03770427〉, articles in press, where the optimization problem was solved under only one linear constraint. This is of interest for solving significant problems pertaining to financial economics as well as some classes of feasibility and optimization problems which frequently occur in tomography and other fields. The results are illustrated in the problem of optimal portfolio selection and the particular case when the expected return of finance portfolio is certain is discussed

Parameter Uncertainty in Exponential Family Tail Estimation

Actuaries are often faced with the task of estimating tails of loss distributions from just a few observations. Thus estimates of tail probabilities (reinsurance prices) and percentiles (solvency capital requirements) are typically subject to substantial parameter uncertainty. We study the bias and MSE of estimators of tail probabilities and percentiles, with focus on 1-parameter exponential families. Using asymptotic arguments it is shown that tail estimates are subject to significant positive bias. Moreover, the use of bootstrap predictive distributions, which has been proposed in the actuarial literature as a way of addressing parameter uncertainty, is seen to double the estimation bias. A bias corrected estimator is thus proposed. It is then shown that the MSE of the MLE, the parametric bootstrap and the bias corrected estimators only differ in terms of order O(n −2), which provides decision-makers with some flexibility as to which estimator to use. The accuracy of asymptotic methods, even for small samples, is demonstrated exactly for the exponential and related distributions, while other 1-parameter distributions are considered in a simulation study. We argue that the presence of positive bias may be desirable in solvency capital calculations, though not necessarily in pricing problems

A Bayesian approach to the estimation of maps between riemannian manifolds

Let \Theta be a smooth compact oriented manifold without boundary, embedded in a euclidean space and let \gamma be a smooth map \Theta into a riemannian manifold \Lambda. An unknown state \theta \in \Theta is observed via X=\theta+\epsilon \xi where \epsilon>0 is a small parameter and \xi is a white Gaussian noise. For a given smooth prior on \Theta and smooth estimator g of the map \gamma we derive a second-order asymptotic expansion for the related Bayesian risk. The calculation involves the geometry of the underlying spaces \Theta and \Lambda, in particular, the integration-by-parts formula. Using this result, a second-order minimax estimator of \gamma is found based on the modern theory of harmonic maps and hypo-elliptic differential operators.Comment: 20 pages, no figures published version includes correction to eq.s 31, 41, 4

Triboelectric Backgrounds to radio-based UHE Neutrino Exeperiments

The triboelectric effect broadly includes any process in which force applied at a boundary layer results in displacement of surface charge, leading to the generation of an electrostatic potential. Wind blowing over granular surfaces, such as snow, can induce a potential difference, with subsequent coronal discharge. Nanosecond timescale discharges can lead to radio-frequency emissions with characteristics similar to piezoelectric-induced discharges. For Antarctic-sited experiments seeking detection of radio-frequency signals generated by collisions of cosmic rays or neutrinos with atmospheric or englacial molecular targets, triboelectric emissions from the surface pose a potential background. This is particularly true for experiments in which radio antennas are buried ~(1--100) m below the snow surface, and seeking to validate neutrino detection strategies by measurement of down-coming radio-frequency emissions from extensive air showers. Herein, after summarizing extant evidence for wind-induced triboelectric effects previously reported elsewhere, we detail additional analysis using archival data collected with the RICE and AURA experiments at the South Pole. We broadly characterize those radio-frequency emissions based on source location, and time-domain and also frequency-domain characteristics. We find that: a) For wind velocities in excess of 10-12 m/s, triboelectric background triggers can dominate data-taking, b) frequency spectra for triboelectric events are generally shifted to the low-end of the regime to which current radio experiments are typically sensitive (100-200 MHz), c) there is an apparent preference for tribo-electric discharges from metal surface structures, consistent with a model in which localized, above-surface structures provide a repository for transported charge

HMGN1 Modulates Nucleosome Occupancy and DNase I Hypersensitivity at the CpG Island Promoters of Embryonic Stem Cells

Chromatin structure plays a key role in regulating gene expression and embryonic differentiation; however, the factors that determine the organization of chromatin around regulatory sites are not fully known. Here we show that HMGN1, a nucleosome-binding protein ubiquitously expressed in vertebrate cells, preferentially binds to CpG island-containing promoters and affects the organization of nucleosomes, DNase I hypersensitivity, and the transcriptional profile of mouse embryonic stem cells and neural progenitors. Loss of HMGN1 alters the organization of an unstable nucleosome at transcription start sites, reduces the number of DNase I-hypersensitive sites genome wide, and decreases the number of nestin-positive neural progenitors in the subventricular zone (SVZ) region of mouse brain. Thus, architectural chromatin-binding proteins affect the transcription profile and chromatin structure during embryonic stem cell differentiation

Reduced-bias estimator of the Conditional Tail Expectation of heavy-tailed distributions

International audienceSeveral risk measures have been proposed in the literature. In this paper, we focus on the estimation of the Conditional Tail Expectation (CTE). Its asymptotic normality has been first established in the literature under the classical assumption that the second moment of the loss variable is finite, this condition being very restrictive in practical applications. Such a result has been extended by Necir {\it et al.} (2010) in the case of infinite second moment. In this framework, we propose a reduced-bias estimator of the CTE. We illustrate the efficiency of our approach on a small simulation study and a real data analysis

Dynamical Mass Generation in a Finite-Temperature Abelian Gauge Theory

We write down the gap equation for the fermion self-energy in a finite-temperature abelian gauge theory in three dimensions. The instantaneous approximation is relaxed, momentum-dependent fermion and photon self-energies are considered, and the corresponding Schwinger-Dyson equation is solved numerically. The relation between the zero-momentum and zero-temperature fermion self-energy and the critical temperature T_c, above which there is no dynamical mass generation, is then studied. We also investigate the effect which the number of fermion flavours N_f has on the results, and we give the phase diagram of the theory with respect to T and N_f.Comment: 20 LaTeX pages, 4 postscript figures in a single file, version to appear in Physical Review

The alteration history of the Jbilet Winselwan CM carbonaceous chondrite: An analog for C‐type asteroid sample return

Jbilet Winselwan is one of the largest CM carbonaceous chondrites available for study. Its light, major, and trace elemental compositions are within the range of other CM chondrites. Chondrules are surrounded by dusty rims and set within a matrix of phyllosilicates, oxides, and sulfides. Calcium‐ and aluminum‐rich inclusions (CAIs) are present at ≤1 vol% and at least one contains melilite. Jbilet Winselwan is a breccia containing diverse lithologies that experienced varying degrees of aqueous alteration. In most lithologies, the chondrules and CAIs are partially altered and the metal abundance is low (<1 vol%), consistent with petrologic subtypes 2.7–2.4 on the Rubin et al. (2007) scale. However, chondrules and CAIs in some lithologies are completely altered suggesting more extensive hydration to petrologic subtypes ≤2.3. Following hydration, some lithologies suffered thermal metamorphism at 400–500 °C. Bulk X‐ray diffraction shows that Jbilet Winselwan consists of a highly disordered and/or very fine‐grained phase (73 vol%), which we infer was originally phyllosilicates prior to dehydration during a thermal metamorphic event(s). Some aliquots of Jbilet Winselwan also show significant depletions in volatile elements such as He and Cd. The heating was probably short‐lived and caused by impacts. Jbilet Winselwan samples a mixture of hydrated and dehydrated materials from a primitive water‐rich asteroid. It may therefore be a good analog for the types of materials that will be encountered by the Hayabusa‐2 and OSIRIS‐REx asteroid sample‐return missions

Neutrino - nucleon reaction rates in the supernova core in the relativistic random phase approximation

In view of the application to supernova simulations, we calculate neutrino reaction rates with nucleons via the neutral and charged currents in the supernova core in the relativistic random phase approximation (RPA) and study their effects on the opacity of the supernova core. The formulation is based on the Lagrangian employed in the calculation of nuclear equation of state (EOS) in the relativistic mean field theory (RMF). The nonlinear meson terms are treated appropriately so that the consistency of the density correlation derived in RPA with the thermodynamic derivative obtained from EOS by RMF is satisfied in the static and long wave length limit. We employ pion and rho meson exchange interactions together with the phenomenological Landau-Migdal parameters for the isospin-dependent nuclear interactions. We find that both the charged and neutral current reaction rates are suppressed from the standard Bruenn's approximate formula considerably in the high density regime. In the low density regime, on the other hand, the vector current contribution to the neutrino-nucleon scattering rate is enhanced in the vicinity of the boundary of the liquid-gas phase transition, while the other contributions are moderately suppressed there also. In the high temperature regime or in the regime where electrons have a large chemical potential, the latter of which is important only for the electron capture process and its inverse process, the recoil of nucleons cannot be neglected and further reduces the reaction rates with respect to the standard approximate formula which discards any energy transfer in the processes. These issues could have a great impact on the neutrino heating mechanism of collapse-driven supernovae.Comment: 16pages, 19figures, submitted to PR