Jan Pospíšil

Practical approaches to Grid workload and resource management in the EGEE project

Resource management and scheduling of distributed, data-driven applications in a Grid environment are challenging problems. Although significant results were achieved in the past few years, the development and the proper deployment of generic, reliable, standard components present issues that still need to be completely solved. Interested domains include workload management, resource discovery, resource matchmaking and brokering, accounting, authorization policies, resource access, reliability and dependability. The evolution towards a service-oriented architecture, supported by emerging standards, is another activity that will demand attention. All these issues are being tackled within the EU-funded EGEE project (Enabling Grids for E-science in Europe), whose primary goals are the provision of robust middleware components and the creation of a reliable and dependable Grid infrastructure to support e-Science applications. In this paper we present the plans and the preliminary activities aiming at providing adequate workload and resource management components, suitable to be deployed in a production-quality Grid.

ASYMPTOTIC PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATOR FOR STOCHASTIC PARABOLIC EQUATIONS WITH ADDITIVE FRACTIONAL BROWNIAN MOTION

A parameter estimation problem is considered for a diagonaliazable stochastic evolution equation using a finite number of the Fourier coefficients of the solution. The equation is driven by additive noise that is white in space and fractional in time with the Hurst parameter

The DataGrid Workload Management System: Challenges and Results

H\geq 1/2

Parameter Estimates and Exact Variations for Stochastic Heat Equations Driven by Space-Time White Noise

. The objective is to study asymptotic properties of the maximum likelihood estimator as the number of the Fourier coefficients increases. A necessary and sufficient condition for consistency and asymptotic normality is presented in terms of the eigenvalues of the operators in the equation.

gLite job provenance

The workload management task of the DataGrid project was mandated to define and implement a suitable architecture for distributed scheduling and resource management in a Grid environment. The result was the design and implementation of a Grid Workload Management System, a super-scheduler with the distinguishing property of being able to take data access requirements into account when scheduling jobs to the available Grid resources. Many novel issues in various fields were faced such as resource management, resource reservation and co-allocation, Grid accounting. In this paper, the architecture and the functionality provided by the DataGrid Workload Management System are presented.

Distributed Tracking, Storage, and Re-use of Job State Information on the Grid

Abstract In this article we calculate the exact quadratic variation in space and quartic variation in time for the solutions to a one dimensional stochastic heat equation driven by a multiplicative space-time white noise. We use the knowledge of exact variations to estimate the drift parameter appearing in the equation.

On calibration of stochastic and fractional stochastic volatility models

The Job Provenance (JP) service is designed to automate keeping track of computations on large scale Grids, giving thus users a tool to correctly archive information about their jobs and to re-submit any job in a reconstructed environment. JP provides a permanent minimal record of job (and its environment) related information, to which free-form user annotations can be added. JP also offers the capability of configuring any number of indexed logical views on the large collections of raw data, allowing efficient processing of even complex user queries selecting on both system data and the annotations. The scalable architecture, capable to handle millions of jobs in a single JP installation, and integrated into the EGEE gLite middleware environment is presented.

Market calibration under a long memory stochastic volatility model

The Logging and Bookkeeping service tracks jobs passing through the Grid. It collects important events generated by both the grid middleware components and applications, and processes them at a chosen LB server to provide the job state. The events are transported through secure and reliable channels. Job tracking is fully distributed and does not depend on a single information source, the robustness is achieved through speculative job state computation in case of reordered, delayed or lost events. The state computation is easily adaptable to modified job control flow.

A uniform job monitoring service in multiple job universes

In this paper we study optimization techniques for calibration of stochastic volatility models to real market data. Several optimization techniques are compared and used in order to solve the nonlinear least squares problem arising in the minimization of the difference between the observed market prices and the model prices. To compare several approaches we use a popular stochastic volatility model firstly introduced by Heston (1993) and a more complex model with jumps in the underlying and approximative fractional volatility. Calibration procedures are performed on two main data sets that involve traded DAX index options. We show how well both models can be fitted to a given option price surface. The routines alongside models are also compared in terms of out-of-sample errors. For the calibration tasks without having a good knowledge of the market (e.g. a suitable initial model parameters) we suggest an approach of combining local and global optimizers. This way we are able to retrieve superior error measures for all considered tasks and models.

Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure

ABSTRACT In this article, we study a long memory stochastic volatility model (LSV), under which stock prices follow a jump-diffusion stochastic process and its stochastic volatility is driven by a continuous-time fractional process that attains a long memory. LSV model should take into account most of the observed market aspects and unlike many other approaches, the volatility clustering phenomenon is captured explicitly by the long memory parameter. Moreover, this property has been reported in realized volatility time-series across different asset classes and time periods. In the first part of the article, we derive an alternative formula for pricing European securities. The formula enables us to effectively price European options and to calibrate the model to a given option market. In the second part of the article, we provide an empirical review of the model calibration. For this purpose, a set of traded FTSE 100 index call options is used and the long memory volatility model is compared to a popular pricing approach – the Heston model. To test stability of calibrated parameters and to verify calibration results from previous data set, we utilize multiple data sets from NYSE option market on Apple Inc. stock.