Drift dependence of optimal trade execution strategies under transient price impact

We give a complete solution to the problem of minimizing the expected liquidity costs in presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that this problem is well-posed only if the drift is absolutely continuous. Optimal strategies often do not exist, and when they do, they depend strongly on the derivative of the drift. Our approach uses elements from singular stochastic control, even though the problem is essentially non-Markovian due to the transience of price impact and the lack in Markovian structure of the underlying price process. As a corollary, we give a complete solution to the minimization of a certain cost-risk criterion in our setting

Dynamic PRA: an Overview of New Algorithms to Generate, Analyze and Visualize Data

State of the art PRA methods, i.e. Dynamic PRA (DPRA) methodologies, largely employ system simulator codes to accurately model system dynamics. Typically, these system simulator codes (e.g., RELAP5 ) are coupled with other codes (e.g., ADAPT, RAVEN that monitor and control the simulation. The latter codes, in particular, introduce both deterministic (e.g., system control logic, operating procedures) and stochastic (e.g., component failures, variable uncertainties) elements into the simulation. A typical DPRA analysis is performed by: 1. Sampling values of a set of parameters from the uncertainty space of interest 2. Simulating the system behavior for that specific set of parameter values 3. Analyzing the set of simulation runs 4. Visualizing the correlations between parameter values and simulation outcome Step 1 is typically performed by randomly sampling from a given distribution (i.e., Monte-Carlo) or selecting such parameter values as inputs from the user (i.e., Dynamic Event Tre

An Optimal Execution Problem with Market Impact

We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that right-continuity at the time origin is associated with the strength of market impact for large sales, otherwise the value function is continuous. Moreover, we show the semi-group property (Bellman principle) and characterise the value function as a viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. We introduce some examples where the forms of the optimal strategies change completely, depending on the amount of the trader's security holdings and where optimal strategies in the Black-Scholes type market with nonlinear market impact are not block liquidation but gradual liquidation, even when the trader is risk-neutral.Comment: 36 pages, 8 figures, a modified version of the article "An optimal execution problem with market impact" in Finance and Stochastics (2014

Proper orthogonal decomposition of solar photospheric motions

The spatio-temporal dynamics of the solar photosphere is studied by performing a Proper Orthogonal Decomposition (POD) of line of sight velocity fields computed from high resolution data coming from the MDI/SOHO instrument. Using this technique, we are able to identify and characterize the different dynamical regimes acting in the system. Low frequency oscillations, with frequencies in the range 20-130 microHz, dominate the most energetic POD modes (excluding solar rotation), and are characterized by spatial patterns with typical scales of about 3 Mm. Patterns with larger typical scales of 10 Mm, are associated to p-modes oscillations at frequencies of about 3000 microHz.Comment: 8 figures in jpg in press on PR

MIRTO: a prototype for real-time ionospheric imaging over the Mediterranean area

MIRTO (Mediterranean Ionosphere with Real-time TOmography) is a collaborative project between Istituto Nazionale di Geofisica (INGV) of Rome, the University of Bath (U.K.) and the Istituto Fisica Applicata «Nello Carrara»-Consiglio Nazionale delle Ricerche (IFAC-CNR) of Florence. The goal of the project is the development of a prototype for real-time imaging of the ionosphere over the Italian region with extension to the Mediterranean Sea. MIRTO uses an original imaging technique developed at the University of Bath and upgraded for real-time use in cooperation with IFAC. The prototype makes use of the data acquired by the real-time ionospheric and geodetic instrumentation operated by INGV. Such measurements drive the imaging algorithm to produce the image of electron density as well as maps and movies of the Total Electron Content (TEC) over the considered area

Pricing and Hedging Asian Basket Options with Quasi-Monte Carlo Simulations

In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We assume a Black-Scholes market with time-dependent volatilities and show how to compute the deltas by the aid of the Malliavin Calculus, extending the procedure employed by Montero and Kohatsu-Higa (2003). Efficient path-generation algorithms, such as Linear Transformation and Principal Component Analysis, exhibit a high computational cost in a market with time-dependent volatilities. We present a new and fast Cholesky algorithm for block matrices that makes the Linear Transformation even more convenient. Moreover, we propose a new-path generation technique based on a Kronecker Product Approximation. This construction returns the same accuracy of the Linear Transformation used for the computation of the deltas and the prices in the case of correlated asset returns while requiring a lower computational time. All these techniques can be easily employed for stochastic volatility models based on the mixture of multi-dimensional dynamics introduced by Brigo et al. (2004).Comment: 16 page

Long-term trends in the ionosphere and upper atmosphere parameters

The first part of the paper is directed to the investigation of the practical importance of possible longterm trends in the F2-layer for ionospheric prediction models. Using observations of about 50 different ionosonde stations with more than 30 years data series of foF2 and hmF2, trends have been derived with the solar sunspot number R12 as index of the solar activity. The final result of this trend analysis is that the differences between the trends derived from the data of the individual stations are relatively large, the calculated global mean values of the foF2 and hmF2 trends, however, are relatively small. Therefore, these small global trends can be neglected for practical purposes and must not be considered in ionospheric prediction models. This conclusion is in agreement with the results of other investigations analyzing data of globally distributed stations. As shown with the data of the ionosonde station Tromsø, however, at individual stations the ionospheric trends may be markedly stronger and lead to essential effects in ionospheric radio propagation. The second part of the paper deals with the reasons for possible trends in the Earth’s atmo- and ionosphere as investigated by different methods using characteristic parameters of the ionospheric D-, E-, and F-regions. Mainly in the F2-region different analyses have been carried out. The derived trends are mainly discussed in connection with an increasing greenhouse effect or by long-term changes in geomagnetic activity. In the F1-layer the derived mean global trend in foF1 is in good agreement with model predictions of an increasing greenhouse effect. In the E-region the derived trends in foE and h´E are compared with model results of an atmospheric greenhouse effect, or explained by geomagnetic effects or other anthropogenic disturbances. The trend results in the D-region derived from ionospheric reflection height and absorption measurements in the LF, MF and HF ranges can at least partly be explained by an increasing atmospheric greenhouse effect

Readout of GEM Detectors Using the Medipix2 CMOS Pixel Chip

We have operated a Medipix2 CMOS readout chip, with amplifying, shaping and charge discriminating front-end electronics integrated on the pixel-level, as a highly segmented direct charge collecting anode in a three-stage gas electron multiplier (Triple-GEM) to detect the ionization from $^{55}$Fe X-rays and electrons from $^{106}$Ru. The device allows to perform moderate energy spectroscopy measurements (20 % FWHM at 5.9 keV $X$-rays) using only digital readout and two discriminator thresholds. Being a truly 2D-detector, it allows to observe individual clusters of minimum ionizing charged particles in $Ar/CO_2$ (70:30) and $He/CO_2$ (70:30) mixtures and to achieve excellent spatial resolution for position reconstruction of primary clusters down to $\sim 50 \mu m$, based on the binary centroid determination method.Comment: 18 pages, 14 pictures. submitted to Nuclear Instruments and Methods in Physics Research

Core-mantle boundary deformations and J2 variations resulting from the 2004 Sumatra earthquake

The deformation at the core-mantle boundary produced by the 2004 Sumatra earthquake is investigated by means of a semi-analytic theoretical model of global coseismic and postseismic deformation, predicting a millimetric coseismic perturbation over a large portion of the core-mantle boundary. Spectral features of such deformations are analysed and discussed. The time-dependent postseismic evolution of the elliptical part of the gravity field (J2) is also computed for different asthenosphere viscosity models. Our results show that, for asthenospheric viscosities smaller than 10^18 Pa s, the postseismic J2 variation in the next years is expected to leave a detectable signal in geodetic observations.Comment: 14 pages, 8 figures, 1 table. It will appear in Geophysical Journal Internationa