FPGA Acceleration of Monte Carlo-based Financial Simulation: Design Challenges and Lessons Learnt

The simulation of interest rate derivatives is a powerful tool to face the current market fluctuations. However, the complexity of the financial models and the way they are processed require exorbitant computation times, what is in clear conflict with the need of a processing time as short as possible to operate in the financial market. To shorten the computation time of financial derivatives the use of hardware accelerators becomes a must.

A stochastic model updating method for parameter variability quantification based on response surface models and Monte Carlo simulation

Stochastic model updating must be considered for quantifying uncertainties inherently existing in real-world engineering structures. By this means the statistical properties,instead of deterministic values, of structural parameters can be sought indicating the parameter variability. However, the implementation of stochastic model updating is much more complicated than that of deterministic methods particularly in the aspects of theoretical complexity and low computational efficiency. This study attempts to propose a simple and cost-efficient method by decomposing a stochastic updating process into a series of deterministic ones with the aid of response surface models and Monte Carlo simulation. The response surface models are used as surrogates for original FE models in the interest of programming simplification, fast response computation and easy inverse optimization. Monte Carlo simulation is adopted for generating samples from the assumed or measured probability distributions of responses. Each sample corresponds to an individual deterministic inverse process predicting the deterministic values of parameters. Then the parameter means and variances can be statistically estimated based on all the parameter predictions by running all the samples. Meanwhile, the analysis of variance approach is employed for the evaluation of parameter variability significance. The proposed method has been demonstrated firstly on a numerical beam and then a set of nominally identical steel plates tested in the laboratory. It is found that compared with the existing stochastic model updating methods, the proposed method presents similar accuracy while its primary merits consist in its simple implementation and cost efficiency in response computation and inverse optimization.

Massively parallelizable list-mode reconstruction using a Monte Carlo-based elliptical Gaussian model

Purpose: A fully three-dimensional (3D) massively parallelizable list-mode ordered-subsets expectation-maximization (LM-OSEM) reconstruction algorithm has been developed for high-resolution PET cameras. System response probabilities are calculated online from a set of parameters derived from Monte Carlo simulations. The shape of a system response for a given line of response (LOR) has been shown to be asymmetrical around the LOR. This work has been focused on the development of efficient region-search techniques to sample the system response probabilities, which are suitable for asymmetric kernel models, including elliptical Gaussian models that allow for high accuracy and high parallelization efficiency. The novel region-search scheme using variable kernel models is applied in the proposed PET reconstruction algorithm. Methods: A novel region-search technique has been used to sample the probability density function in correspondence with a small dynamic subset of the field of view that constitutes the region of response (ROR). The ROR is identified around the LOR by searching for any voxel within a dynamically calculated contour. The contour condition is currently defined as a fixed threshold over the posterior probability, and arbitrary kernel models can be applied using a numerical approach. The processing of the LORs is distributed in batches among the available computing devices, then, individual LORs are processed within different processing units. In this way, both multicore and multiple many-core processing units can be efficiently exploited. Tests have been conducted with probability models that take into account the noncolinearity, positron range, and crystal penetration effects, that produced tubes of response with varying elliptical sections whose axes were a function of the crystal's thickness and angle of incidence of the given LOR. The algorithm treats the probability model as a 3D scalar field defined within a reference system aligned with the ideal LOR. Results: This new technique provides superior image quality in terms of signal-to-noise ratio as compared with the histogram-mode method based on precomputed system matrices available for a commercial small animal scanner. Reconstruction times can be kept low with the use of multicore, many-core architectures, including multiple graphic processing units. Conclusions: A highly parallelizable LM reconstruction method has been proposed based on Monte Carlo simulations and new parallelization techniques aimed at improving the reconstruction speed and the image signal-to-noise of a given OSEM algorithm. The method has been validated using simulated and real phantoms. A special advantage of the new method is the possibility of defining dynamically the cut-off threshold over the calculated probabilities thus allowing for a direct control on the trade-off between speed and quality during the reconstruction.

Student academic performance stochastic simulator based on the Monte Carlo method

In this paper, a computer-based tool is developed to analyze student performance along a given curriculum. The proposed software makes use of historical data to compute passing/failing probabilities and simulates future student academic performance based on stochastic programming methods (MonteCarlo) according to the specific university regulations. This allows to compute the academic performance rates for the specific subjects of the curriculum for each semester, as well as the overall rates (the set of subjects in the semester), which are the efficiency rate and the success rate. Additionally, we compute the rates for the Bachelors degree, which are the graduation rate measured as the percentage of students who finish as scheduled or taking an extra year and the efficiency rate (measured as the percentage of credits of the curriculum with respect to the credits really taken). In Spain, these metrics have been defined by the National Quality Evaluation and Accreditation Agency (ANECA). Moreover, the sensitivity of the performance metrics to some of the parameters of the simulator is analyzed using statistical tools (Design of Experiments). The simulator has been adapted to the curriculum characteristics of the Bachelor in Engineering Technologies at the Technical University of Madrid(UPM).

Orthogonal MCMC algorithms

Monte Carlo (MC) methods are widely used in signal processing, machine learning and stochastic optimization. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In this work, we introduce a novel parallel interacting MCMC scheme, where the parallel chains share information using another MCMC technique working on the entire population of current states. These parallel ?vertical? chains are led by random-walk proposals, whereas the ?horizontal? MCMC uses a independent proposal, which can be easily adapted by making use of all the generated samples. Numerical results show the advantages of the proposed sampling scheme in terms of mean absolute error, as well as robustness w.r.t. to initial values and parameter choice.

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

We review the main results from extensive Monte Carlo (MC) simulations on athermal polymer packings in the bulk and under confinement. By employing the simplest possible model of excluded volume, macromolecules are represented as freely-jointed chains of hard spheres of uniform size. Simulations are carried out in a wide concentration range: from very dilute up to very high volume fractions, reaching the maximally random jammed (MRJ) state. We study how factors like chain length, volume fraction and flexibility of bond lengths affect the structure, shape and size of polymers, their packing efficiency and their phase behaviour (disorder–order transition). In addition, we observe how these properties are affected by confinement realized by flat, impenetrable walls in one dimension. Finally, by mapping the parent polymer chains to primitive paths through direct geometrical algorithms, we analyse the characteristics of the entanglement network as a function of packing density.

Simulation using the Monte Carlo method

Photocopy. Springfield, Va., Distributed by Clearinghouse for Federal Scientific and Technical Information [1969]

Adsorption of Supercritical fluids on graphitised thermal carbon black: Molecular layer structure theory versus grand canonical Monte Carlo simulation

This paper presents a detailed analysis of adsorption of supercritical fluids on nonporous graphitized thermal carbon black. Two methods are employed in the analysis. One is the molecular layer structure theory (MLST), proposed recently by our group, and the other is the grand canonical Monte Carlo (GCMC) simulation. They were applied to describe the adsorption of argon, krypton, methane, ethylene, and sulfur hexafluoride on graphitized thermal carbon black. It was found that the MLST describes all the experimental data at various temperatures well. Results from GCMC simulations describe well the data at low pressure but show some deviations at higher pressures for all the adsorbates tested. The question of negative surface excess is also discussed in this paper.

Grand canonical Monte Carlo simulation study of methane adsorption at an open graphite surface and in slitlike carbon pores at 273 K

Grand canonical Monte Carlo (GCMC) simulation was used for the systematic investigation of the supercritical methane adsorption at 273 K on an open graphite surface and in slitlike micropores of different sizes. For both considered adsorption systems the calculated excess adsorption isotherms exhibit a maximum. The effect of the pore size on the maximum surface excess and isosteric enthalpy of adsorption for methane storage at 273 K is discussed. The microscopic detailed picture of methane densification near the homogeneous graphite wall and in slitlike pores at 273 K is presented with selected local density profiles and snapshots. Finally, the reliable pore size distributions, obtained in the range of the microporosity, for two pitch-based microporous activated carbon fibers are calculated from the local excess adsorption isotherms obtained via the GCMC simulation. The current systematic study of supercritical methane adsorption both on an open graphite surface and in slitlike micropores performed by the GCMC summarizes recent investigations performed at slightly different temperatures and usually a lower pressure range by advanced methods based on the statistical thermodynamics.

Application of Monte Carlo simulations to identify an appropriate dosage strategy for patients receiving a continuous intravenous infusion of enoxaparin

Aim: To identify an appropriate dosage strategy for patients receiving enoxaparin by continuous intravenous infusion (CII). Methods: Monte Carlo simulations were performed in NONMEM, (200 replicates of 1000 patients) to predict steady state anti-Xa concentrations (Css) for patients receiving a CII of enoxaparin. The covariate distribution model was simulated based on covariate demographics in the CII study population. The impact of patient weight, renal function (creatinine clearance (CrCL)) and patient location (intensive care unit (ICU)) were evaluated. A population pharmacokinetic model was used as the input-output model (1-compartment first order output model with mixed residual error structure). Success of a dosing regimen was based on the percent of Css that is between the therapeutic range of 0.5 IU/ml to 1.2 IU/ml. Results: The best dose for patients in the ICU was 4.2IU/kg/h (success mean 64.8% and 90% prediction interval (PI): 60.1–69.8%) if CrCL60ml/min, the best dose was 8.3IU/kg/h (success mean 65.4%, 90% PI: 58.5–73.2%). Simulations suggest that there was a 50% improvement in the success of the CII if the dose rate for ICU patients with CrCL

Productivity change using growth accounting and frontier-based approaches:evidence from a Monte Carlo analysis

This study presents some quantitative evidence from a number of simulation experiments on the accuracy of the productivitygrowth estimates derived from growthaccounting (GA) and frontier-based methods (namely data envelopment analysis-, corrected ordinary least squares-, and stochastic frontier analysis-based malmquist indices) under various conditions. These include the presence of technical inefficiency, measurement error, misspecification of the production function (for the GA and parametric approaches) and increased input and price volatility from one period to the next. The study finds that the frontier-based methods usually outperform GA, but the overall performance varies by experiment. Parametric approaches generally perform best when there is no functional form misspecification, but their accuracy greatly diminishes otherwise. The results also show that the deterministic approaches perform adequately even under conditions of (modest) measurement error and when measurement error becomes larger, the accuracy of all approaches (including stochastic approaches) deteriorates rapidly, to the point that their estimates could be considered unreliable for policy purposes.

A New Algorithm for Monte Carlo for American Options

2000 Mathematics Subject Classification: 91B28, 65C05.

Monte Carlo Study of Particle Transport Problem in Air Pollution

2002 Mathematics Subject Classification: 65C05.

Some Inequalities of the Uniform Ergodicity and Strong Stability of Homogeneous Markov Chains

2000 Mathematics Subject Classification: 60J45, 60K25

Monte Carlo Method for Reconstruction of Densities

2000 Mathematics Subject Classification: 65C05