Full Monte Carlo Method Research Articles

Pricing arithmetic Asian options under jump diffusion CIR processes

We compute analytical formulae for pricing arithmetic Asian options under jump diffusion CIR processes. To derive the solution, we employ a characteristic function of the underlying asset price process and its integrated process that is not required to take the inversion Fourier or Laplace transform. We conduct numerical tests for validation of proposed formulae to confirm that they provide stable and accurate option prices with much faster computation time than the full Monte Carlo method.

CATASTROPHE INSURANCE DERIVATIVES PRICING USING A COX PROCESS WITH JUMP DIFFUSION CIR INTENSITY

We propose an analytical pricing method for stop-loss reinsurance contracts and catastrophe insurance derivatives using a Cox process with jump diffusion Cox–Ingersoll–Ross (CIR) intensity. The expected payoff of these contracts is expressed by the Laplace transform of the integration of the jump diffusion CIR process and the first moment of the aggregate loss. To confirm that the proposed analytical formula provides stable and accurate insurance derivative prices, we simulate them using a full Monte Carlo method compared to those obtained from its theoretical expectation. It shows that it is much faster way to obtain them than the full Monte Carlo method. We also conduct sensitivity analysis by changing the relevant parameters in the loss intensity providing their figures.

Steel Moment-Resisting Frame Reliability via the Interval Analysis by FCM-PSO Approach considering Various Uncertainties

ABSTRACTOne important issue in compiling siesmic fragility curves is blending and incorporating uncertainties into the model under seismic conditions. Methods used in this regard are either approximate, costly and time-consuming. To address this, the optimized fuzzy method is used. To compile the fragility curve, epistemic and aleatory uncertainties have been incorporated in which model parameters are fuzzy values and FCM-PSO method is used to estimate mean and standard deviation of fragility curve. The FCM-PSO algorithm is trained using scenarios compiled via the IDA method. Results obtained from the full Monte Carlo method were used for verification. The method employed here is advantageous with regard to both accuracy and execution time.

Application of dose kernel calculation using a simplified Monte Carlo method to treatment plan for scanned proton beams.

Full Monte Carlo (FMC) calculation of dose distribution has been recognized to have superior accuracy, compared with the pencil beam algorithm (PBA). However, since the FMC methods require long calculation time, it is difficult to apply them to routine treatment planning at present. In order to improve the situation, a simplified Monte Carlo (SMC) method has been introduced to the dose kernel calculation applicable to dose optimization procedure for the proton pencil beam scanning. We have evaluated accuracy of the SMC calculation by comparing a result of the dose kernel calculation using the SMC method with that using the FMC method in an inhomogeneous phantom. The dose distribution obtained by the SMC method was in good agreement with that obtained by the FMC method. To assess the usefulness of SMC calculation in clinical situations, we have compared results of the dose calculation using the SMC with those using the PBA method for three clinical cases of tumor treatment. The dose distributions calculated with the PBA dose kernels appear to be homogeneous in the planning target volumes (PTVs). In practice, the dose distributions calculated with the SMC dose kernels with the spot weights optimized with the PBA method show largely inhomogeneous dose distributions in the PTVs, while those with the spot weights optimized with the SMC method have moderately homogeneous distributions in the PTVs. Calculation using the SMC method is faster than that using the GEANT4 by three orders of magnitude. In addition, the graphic processing unit (GPU) boosts the calculation speed by 13 times for the treatment planning using the SMC method. Thence, the SMC method will be applicable to routine clinical treatment planning for reproduction of the complex dose distribution more accurately than the PBA method in a reasonably short time by use of the GPU‐based calculation engine.PACS number(s): 87.55.Gh

SU‐E‐T‐805: Verification of the Simplified Monte Carlo Method for Simulation in An Inhomogeneous Phantom

Purpose:A simplified Monte Carlo (SMC) method has been developed to obtain fast and accurate dose calculation in heterogeneous tissues to improve the accuracy of dose calculation. We have applied the SMC method to calculation of dose kernels for the pencil beam scanning. While the SMC method tracks individual primary protons in medium, it simplifies the dose calculation by using a measured depth‐dose distribution instead of considering nuclear reactions and tracking secondary particles. To verify the accuracy of SMC calculation, we compared a dose‐calculation Result using the SMC method with that using the Full Monte Carlo (FMC) method in an inhomogeneous phantom.Methods:As a model of the inhomogeneous media, we considered a phantom complied of a rectangular acrylic block of size 150*300*200 mm 3 immersed in water within a virtual container with a size of 300*300*400 mm3.Results:We found excellent agreement of overall dose distributions between the SMC and FMC methods. As for the laterally integrated depth‐dose distributions, slight difference was found in front of the second Bragg‐Peak between the two algorithms. While it took 25717.0 s on 2.7 GHz Intel Core i7 for the FMC method to complete the calculation, it took 15.4 s for the SMC method to complete it. The SMC method can calculate the dose distribution approximately 1675 times faster than the FMC method.Conclusion:The dose distribution obtained by SMC method agreed well that obtained by the FMC method in a simple inhomogeneous phantom. In contrast, calculation time by the SMC method has been reduced by three orders in magnitude compared with the FMC method.

Influence of hadronic interaction models and the cosmic ray spectrum on the high-energy atmospheric muon and neutrino flux

The recent observations of muon charge ratio up to about 10 TeV and of atmospheric neutrinos up to energies of about 400 TeV has triggered a renewed interest into the high-energy interaction models and cosmic ray primary composition. A reviewed calculation of lepton spectra produced in cosmic ray induced extensive air showers is carried out with a primary cosmic ray spectrum that fits the latest direct measurements below the knee. In order to achieve this, we used a full Monte Carlo method to derive the inclusive differential spectra (yields) of muons, muon neutrinos and electron neutrinos at the surface for energies between 80 GeV and hundreds of PeV. Using these results the differential flux and the flavor ratios of leptons were calculated. The air shower simulator CORSIKA 6.990 was used for showering and propagation of the secondary particles through the atmosphere, employing the established high energy hadronic interaction models SIBYLL 2.1, QGSJet-01 and QGSJet-II-03. We show that the performance of the interaction models allows makes it possible to predict the spectra within experimental uncertainties, while SIBYLL generally yields a higher flux at the surface than the QGSJet models. The calculation of the flavor and charge ratios has lead to inconsistent results, mainly influenced by the different representations of the K/π ratio within the models. The influence of the knee of cosmic rays is reflected in the secondary spectra at energies between 100 and 200 TeV. Furthermore, we could quantify systematic uncertainties of atmospheric muon- and neutrino fluxes, associated to the models of the primary cosmic ray spectrum and the interaction models. For most recent parametrizations of the cosmic ray primary spectrum, atmospheric muons can be determined with an uncertainty smaller than +15/-13% of the average flux. Uncertainties of the muon and electron neutrino fluxes can be calculated within an average error of +32/-22% and +25/-19%, respectively. See the published paper [1].

Influence of hadronic interaction models and the cosmic ray spectrum on the high-energy atmospheric muon and neutrino flux

The recent observations of muon charge ratio up to about 10 TeV and of atmospheric neutrinos up to energies of about 400 TeV has triggered a renewed interest into the high-energy interaction models and cosmic ray primary composition. A reviewed calculation of lepton spectra produced in cosmic ray induced extensive air showers is carried out with a primary cosmic ray spectrum that fits the latest direct measurements below the knee. In order to achieve this, we used a full Monte Carlo method to derive the inclusive differential spectra (yields) of muons, muon neutrinos and electron neutrinos at the surface for energies between 80 GeV and hundreds of PeV. Using these results the differential flux and the flavor ratios of leptons were calculated. The air shower simulator CORSIKA 6.990 was used for showering and propagation of the secondary particles through the atmosphere, employing the established high energy hadronic interaction models SIBYLL 2.1, QGSJet-01 and QGSJet-II-03. We show that the performance of the interaction models allows makes it possible to predict the spectra within experimental uncertainties, while SIBYLL generally yields a higher flux at the surface than the QGSJet models. The calculation of the flavor and charge ratios has lead to inconsistent results, mainly influenced by the different representations of the K/π ratio within the models. The influence of the knee of cosmic rays is reflected in the secondary spectra at energies between 100 and 200 TeV. Furthermore, we could quantify systematic uncertainties of atmospheric muon- and neutrino fluxes, associated to the models of the primary cosmic ray spectrum and the interaction models. For most recent parametrizations of the cosmic ray primary spectrum, atmospheric muons can be determined with an uncertainty smaller than +15/-13% of the average flux. Uncertainties of the muon and electron neutrino fluxes can be calculated within an average error of +32/-22% and +25/-19%, respectively. See the published paper [1].

Influence of hadronic interaction models and the cosmic ray spectrum on the high energy atmospheric muon and neutrino flux

The recent observations of muon charge ratio up to about 10 TeV and of atmospheric neutrinos up to energies of about 400 TeV have triggered a renewed interest into the high-energy interaction models and cosmic-ray primary composition. A reviewed calculation of lepton spectra produced in cosmic-ray-induced extensive air showers is carried out with a primary cosmic-ray spectrum that fits the latest direct measurements below the knee. In order to achieve this, we used a full Monte Carlo method to derive the inclusive differential spectra (yields) of muons, muon neutrinos and electron neutrinos at the surface for energies between 80 GeV and hundreds of PeV. Using these results, the differential flux and the flavor ratios of leptons were calculated. The air shower simulator CORSIKA 6.990 was used for showering and propagation of the secondary particles through the atmosphere, employing the established high-energy hadronic interaction models SIBYLL 2.1, QGSJet-01 and QGSJet-II-03. We show that the performance of the interaction models makes it possible to predict the spectra within experimental uncertainties, while SIBYLL generally yields a higher flux at the surface than the QGSJet models. The calculation of the flavor and charge ratios has lead to inconsistent results, mainly influenced by the different representations of the $K/\ensuremath{\pi}$ ratio within the models. The influence of the knee of cosmic rays is reflected in the secondary spectra at energies between 100 and 200 TeV. Furthermore, we could quantify systematic uncertainties of atmospheric muon and neutrino fluxes, associated to the models of the primary cosmic-ray spectrum and the interaction models. For most recent parametrizations of the cosmic-ray primary spectrum, atmospheric muons can be determined with an uncertainty smaller than $\genfrac{}{}{0}{}{+15}{\ensuremath{-}13}%$ of the average flux. Uncertainties of the muon and electron neutrino fluxes can be calculated within an average error of $\genfrac{}{}{0}{}{+32}{\ensuremath{-}22}%$ and $\genfrac{}{}{0}{}{+25}{\ensuremath{-}19}%$, respectively.

A Monte Carlo Method for Calculation of the Dynamic Behaviour of Nuclear Reactors

In safety calculations of nuclear reactors, dynamic calculations are of great interest. This type of calculation is mainly done by making an approximation and then using a deterministic code to solve the simplified problem. In this paper a full Monte Carlo method is proposed to perform these calculations on seconds to minutes scale without approximations. First the sampling of precursor decay is needed. The decay of precursors plays a crucial role in the dynamics of nuclear reactors, but the lifetime of a precursor can go up to 10 2 s. This is much larger than the order of the lifetime of a prompt neutron (10 −4 s) or the order of a prompt neutron chain (10 −2 s). Therefore precursors in this simulation are forced to decay according to a modified pdf. This ensures a small variance in the delayed neutron distribution in time. The simulation scheme has also been adapted for dynamic Monte Carlo. The simulation is now divided in time steps and the ancestor of a particle needs to be tracked throughout the simulation for proper variance estimation. After each time step the system properties can be adjusted. Finally the dynamic Monte Carlo method is used to calculate the power production in a simple system. The results agree with a point kinetics calculation of the same problem.

SU‐FF‐T‐441: Application of the Simplified Monte Carlo Algorithm to a Clinical Case for Proton Treatment Planning

Purpose: We have developed a simplified Monte Carlo calculation (SMC) algorithm of dose distribution in proton therapy to improve the accuracy of dose calculations yet with a reasonable calculation time. We verified the new SMC by measurements, applied it to the clinical case, and compared the results with those by the conventional pencil beam algorithm (PBA). Method and Materials: The SMC takes into account the edge‐scattering effects in an aperture and a range‐compensating bolus ignored in the conventional pencil beam algorithm (PBA). In the SMC, since the dose in the human body is calculated using the measured dose distribution in water, the calculation time can be reduced compared with the full Monte Carlo method. To verify the accuracy of the SMC, the dose distribution formed by 235‐MeV protons traversing a step‐shaped bolus were measured with the PTW 2D‐ARRAY detector. We applied the verified SMC to the clinical case and compared with the results obtained by the PBA. Results: While the new SMC reproduced well the measured dose distribution in water of protons traversing the step‐shaped phantom, the PBA could not reproduce the hot spots due to the surface scattering effects of the aperture and the bolus. In the clinical case, while the high‐dose parts at the entrance region and complex dose distributions have been found in the SMC, such dose structures have not been seen in the PBA. The calculation time of the SMC was 20 minutes for simulated 4 mega particles, the calculated voxels of 0.7 mega, the rms statistical error of 4.5%. Conclusion: We verified that the SMC method reproduced well the measured dose distributions with a reasonable calculation time. We applied it to the clinical case and found that a complex dose distribution predicted by the full Monte Carlo method also appears.

Conditional Monte Carlo sampling to find branching architectures of polymers from radical polymerizations with transfer to polymer and recombination termination

A model is developed that predicts branching architectures of polymers from radical polymerization with transfer to polymer and termination by disproportionation and recombination, in a continuously stirred tank reactor (CSTR). It is a so-called conditional Monte Carlo (MC) method generating architectures of molecules of specified dimensions. The relevant dimensions in the present case are the number of branch points, n p, and the number of combined parts a molecule consists of, n c. These branch points and combination points together are decisive for the connectivity inside molecules. The modeling strategy is based on backtracking of the molecular growth history in terms of the chemical events determining connectivity, transfer to polymer and recombination termination. The recombination termination mechanism requires the model to develop parts of the architecture following several paths back to the initial primary polymers that form the starting points for the molecules. The algorithm requires the construction of probability density functions being evaluated using a fast Galerkin-FEM method. The architectures generated by the conditional Monte Carlo method are compared to those from a full MC method using several qualifiers. One of these is the number of initial primary polymers in a molecule as well as their lengths, another is the radius of gyration contraction factor. Perfect agreement is found between the architectures found by the conditional and full MC methods.

Impact of System Design Parameters on Image Figures of Merit for a Mouse PET Scanner

In this study, an analytical simulation model was developed to investigate how system design parameters affect image figures of merit and task performance for small animal positron emission tomography (PET) scanners designed to image mice. For a very high resolution imaging system, important physical effects that may impact image quality are positron range, annihilation photon acollinearity, detector point-spread function (PSF) and coincident photon count levels (i.e., statistical noise). Modeling of these effects was included in an analytical simulation that generated multiple realizations of sinograms with varying levels of each effect. To evaluate image quality with respect to quantitation and detection task performance, four different figures of merit were measured: 1) root mean square error (RMSE); 2) a region of interest SNR (SNR/sub ROI/); 3) nonprewhitening matched filter SNR (SNR/sub NPW/); and 4) recovery coefficient. The results indicate that for very high resolution imaging systems, the increase in positron range of C-11 compared to F-18 radiolabeling causes a significant reduction of quantitation (SNR/sub ROI/) and detection (SNR/sub NPW/) accuracy for small regions. In addition, changing the shape of the detector PSF, which depends on crystal thickness, causes significant variations in quantitation and detection performance. However, while increasing noise levels significantly increase RMSE and decrease detectability (SNR/sub NPW/), the quantitation task performance (SNR/sub ROI/), is less sensitive to noise levels. These results imply that resolution is more important than sensitivity for quantitation task performance, while sensitivity is a more significant issue for detection. The analytical simulation model can be used for estimating task performance of small animal PET systems more rapidly than existing full Monte Carlo methods, although Monte Carlo methods are needed to estimate system parameters.

A simple life-cycle method for predicting extreme shoreline erosion

The dynamical responses of a shoreline over long-term (years or decades) is a non-linear and time-dependent random process. It is affected by both longshore and cross-shore sediment transports. The former tends to cause cumulative changes in the mean shoreline position while the latter usually only leads to beach profile fluctuations relative to the moving mean beach profile. Due to the time-dependency of the process the life-cycle approach is ideally suited to formulate the probability distribution of extreme shoreline erosion. A model based on such approach and using standard Monte Carlo simulation techniques has been reported by Dong and Chen (1999). In this paper a simplified procedure is developed by introducing the assumption that the longshore and cross-shore processes are statistically independent. This then allows the probability distribution of the extreme erosion to be calculated in terms of the marginal probability distributions of the maximum recessions due to purely longshore and purely cross-shore transport. This method was applied to two idealised shoreline configurations and its usefulness for engineering applications is evaluated by comparison with the full Monte Carlo method.

Radiation Shielding for ITER to Allow for Hands-on Maintenance inside the Cryostat (Methodology for Estimating Shutdown Dose Rate in a Complex Geometry)

In the shielding design of the ITER machine, which is a tokamak fusion experimental reactor and has a very complex geometry, it is important to have a reliable estimation of the dose rate levels after reactor shutdown for realising hands-on maintenance around the torus. The ITER project position is that dose rates inside the cryostat be kept low enough to allow for human access shortly after shutdown for limited periods to provide rescue and/or maintenance activities.The methodology of estimation for dose rates after shutdown in such a complex geometry machine is discussed. The Monte Carlo method is preferable to conduct neutron transport calculations in the ITER geometry. The Conversion Factor method, which was used for dose rate estimation in the 1998 ITER shielding design, is described with an example of dose rate estimation around penetrations in the vacuum vessel. A Full Monte Carlo method is proposed showing the possibility of eliminating uncertainty accompanied with conversion factors from neutron flux or isotope production rate to dose rate after shutdown.

Modeling of shot noise in x-ray photoresist exposure

New photoresist technologies yielding higher resist sensitivities together with the greater photon energies inherent in x-ray lithography put lithography systems closer and closer to the shot noise limit. Thus there is a need to address the effects of shot noise on resist exposure. We will present the description of a stochastic model, and its implementation in a simulator, which emulates the exposure process by effecting what amounts to a photon-by-photon treatment of the problem, thereby taking into account the effects of shot noise. The model starts with an aerial image, computed using a deterministic model based on Fresnel diffraction, interprets it as the probability density function (pdf) for the distribution of the photons. The stochasticity of the process is taken into account by randomly generating a finite number of events (photons) whose distribution follows the pdf. The penetration depths are stochastically predicted according to the appropriate distribution. At the point predicted, the incident energy is redistributed according to a point spread function or a full Monte Carlo method. The superposition of all of the photons provides us with the latent image. The dissolution process is then modeled using a stochastic cell dissolution model. We will present results of practical importance for chemically amplified resist systems and correlate the results with observations made in the laboratory.

A subroutine package for fast simulation of air showers and response of surface detectors

A subroutine package, GENAS, is presented which enables the user to generate air showers induced by gamma rays, protons, or heavy primaries ranging from 10 13 eV to 10 20 eV. GENAS is capable of producing air showers very rapidly while keeping the quality of the showers as if they were produced by the full Monte Carlo method. It includes the response of detectors consisting of a plastic scintillator under thin iron and an optional lead sheet. GENAS offers a means for investigating surface-array performance in a quantitative level.

Cerenkov radiation in air

Simulation of Cerenkov light (0.4-0.67 mu m) from electromagnetic cascades in the atmosphere have been performed for various energies of the primary photon (1014-1016 eV) for vertically incident showers. In the calculations of both cascade development and Cerenkov light production, the full Monte Carlo method has been applied to allow for all processes and for all possible fluctuations. In calculations, the so-called 'thinning method' was used. Differences between these results and those of Zatsepin et al. (1962) are presented. The results of their investigation are compared with experimental data obtained from the very high-energy gamma -ray point research.

Three-dimensional cascade showers in lead taking account of the Landau-Pomeranchuk-Migdal effect

Cascade showers in the ultrahigh-energy region are investigated, by taking into account the Landau-Pomeranchuk-Migdal effect in the processes of bremsstrahlung and pair production by the use of the full Monte Carlo method. Calculations are carried out in both one dimension and three dimensions and mean values, such as numbers of shower particles, mean square angular and lateral spread of particles and lateral structure functions, are obtained. These quantities are compared with results from cascade theory under approximationA and their features are discussed. The validity of the Monte Carlo method adopted is checked in individual processes in a cascade shower and is examined as a whole by comparing results from the simulation with those from the corresponding analytical theory.