• Title, Summary, Keyword: Monte Carlo Method

### EFFICIENT MONTE CARLO ALGORITHM FOR PRICING BARRIER OPTIONS

• Moon, Kyoung-Sook
• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.285-294
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• 2008
• A new Monte Carlo method is presented to compute the prices of barrier options on stocks. The key idea of the new method is to use an exit probability and uniformly distributed random numbers in order to efficiently estimate the first hitting time of barriers. It is numerically shown that the first hitting time error of the new Monte Carlo method decreases much faster than that of standard Monte Carlo methods.

### Evaluation of Probabilistic Finite Element Method in Comparison with Monte Carlo Simulation

• 이재영;고홍석
• Magazine of the Korean Society of Agricultural Engineers
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• v.32 no.E
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• pp.59-66
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• 1990
• Abstract The formulation of the probabilistic finite element method was briefly reviewed. The method was implemented into a computer program for frame analysis which has the same analogy as finite element analysis. Another program for Monte Carlo simulation of finite element analysis was written. Two sample structures were assumed and analized. The characteristics of the second moment statistics obtained by the probabilistic finite element method was examined through numerical studies. The applicability and limitation of the method were also evaluated in comparison with the data generated by Monte Carlo simulation.

### A Study on Generation of Stochastic Rainfall Variation using Multivariate Monte Carlo method (다변량 Monte Carlo 기법을 이용한 추계학적 강우 변동 생성기법에 관한 연구)

• Ahn, Ki-Hong;Han, Kun-Yeun
• Journal of the Korean Society of Hazard Mitigation
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• v.9 no.3
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• pp.127-133
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• 2009
• In this study, dimensionless-cumulative rainfall curves were generated by multivariate Monte Carlo method. For generation of rainfall curve rainfall storms were divided and made into dimensionless type since it was required to remove the spatial and temporal variances as well as differences in rainfall data. The dimensionless rainfall curves were divided into 4 types, and log-ratio method was introduced to overcome the limitations that elements of dimensionless-cumulative rainfall curve should always be more than zero and the sum total should be one. Orthogonal transformation by Johnson system and the constrained non-normal multivariate Monte Carlo simulation were introduced to analyse the rainfall characteristics. The generative technique in stochastic rainfall variation using multivariate Monte Carlo method will contribute to the design and evaluation of hydrosystems and can use the establishment of the flood disaster prevention system.

### Decision of Error Tolerance in Sonar Array by the Monte-Carlo Method (Monte-Carlo 방법에 의한 소나배열 소자의 허용오차 규정)

• 김형동;이용범;이준영
• The Journal of the Acoustical Society of Korea
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• v.21 no.3
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• pp.221-229
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• 2002
• In thin paper, error tolerance of each array element which satisfies error tolerance of beam pattern is decided by using the Monte-Carlo method. Conventional deterministic method decides the error tolerance of each element from the acceptance pattern by testing all cases, but this method is not suitable for the analysis of large number of array elements because the computation resources increase exponentially as the number of array elements increases. To alleviate this problem, we applied new algorithm which reduces the increment of calculation time increased by the number of the array elements. We have validates the determined error tolerance region through several simulation.

### Interference Analysis based on the Monte-Carlo Method (Monte-Carlo 기반의 간섭분석에 관한 연구)

• Kim, Seong-Kweon
• The Journal of the Korea institute of electronic communication sciences
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• v.3 no.2
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• pp.58-64
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• 2008
• In this paper, we proposed the methodology of interference analysis based on monte-carlo method for effective use of Industrial, Scientific, Medical (ISM) band. The interference scenario is divided according to the distance and density. The simulation of interference analysis evaluates the interference probability according to distribution density of Interfering Transmitters (It) in the Secure Interference Area (SIA). The SIA is gained from the Interference Efficiency Range that satisfied to Interference Permissible Range of Victim Receiver (Vr). Simulation result that apply the proposed interference scenario to the WLAN and bluetooth, Interference Permissible Range was 60~400m. And the WLAN was acceptable within interference permissible range to six bluetooth that exist in the SIA. In the same condition, when applied Listen Before Talk (LBT) based on Cognitive Radio (CR) to the bluetooth using Frequency Hopping (FH), interference probability was decreased sharply. The Spectrum Engineering Advanced Monte Carlo Analysis Tool (SEAMCAT) that has been developed based on the monte-carlo method by European Radio-communications Office (ERO) were used to the interference simulation.

### A numerical study of the performance of a turbomolecular pump (터보분자펌프의 성능해석에 관한 수치해석적 연구)

• Hwang, Yeong-Gyu;Heo, Jung-Sik
• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.11
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• pp.3620-3629
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• 1996
• In the free molecular flow range, the pumping performance of a turbomolecular pump has been predicted by calculation of the transmission probability which employs the integral method and the test particle Monte-Carlo method. Also, new approximate method combining the double stage solutions, so called double-approximation, is presented here. The calculated values of transmission probability for the single stage agree quantitatively with the previous known numerical results. For a six-stage pump, the Monte-Carlo method is employed to calculate the overall transmission probability for the entire set of blade rows. When the results of the approximate method combining the single stage solutions are compared with those of the Monte-Carlo method at dimensionless blade velocity ratio C=0.4, the previous known approximate method overestimates as much as 34% than does the Monte-Carlo method. But, the new approximate method gives more accurate results, whose relative error is 10% compared to the Monte-Carlo method, than does the previous approximate method.

### Application of quasi-Monte Carlo methods in multi-asset option pricing (준난수 몬테칼로 방법을 이용한 다중자산 옵션 가격의 추정)

• Mo, Eun Bi;Park, Chongsun
• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.669-677
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• 2013
• Quasi-Monte Carlo method is known to have lower convergence rate than the standard Monte Carlo method. Quasi-Monte Carlo methods are using low discrepancy sequences as quasi-random numbers. They include Halton sequence, Faure sequence, and Sobol sequence. In this article, we compared standard Monte Carlo method, quasi-Monte Carlo methods and three scrambling methods of Owen, Faure-Tezuka, Owen-Faure-Tezuka in valuation of multi-asset European call option through simulations. Moro inversion method is used in generating random numbers from normal distribution. It has been shown that three scrambling methods are superior in estimating option prices regardless of the number of assets, volatility, and correlations between assets. However, there are no big differences between them.

### A new approach to determine batch size for the batch method in the Monte Carlo Eigenvalue calculation

• Lee, Jae Yong;Kim, Do Hyun;Yim, Che Wook;Kim, Jae Chang;Kim, Jong Kyung
• Nuclear Engineering and Technology
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• v.51 no.4
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• pp.954-962
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• 2019
• It is well known that the variance of tally is biased in a Monte Carlo calculation based on the power iteration method. Several studies have been conducted to estimate the real variance. Among them, the batch method, which was proposed by Gelbard and Prael, has been utilized actively in many Monte Carlo codes because the method is straightforward, and it is easy to implement the method in the codes. However, there is a problem when utilizing the batch method because the estimated variance varies depending on batch size. Often, the appropriate batch size is not realized before the completion of several Monte Carlo calculations. This study recognizes this shortcoming and addresses it by permitting selection of an appropriate batch size.

### A Second-Order Design Sensitivity-Assisted Monte Carlo Simulation Method for Reliability Evaluation of the Electromagnetic Devices

• Ren, Ziyan;Koh, Chang-Seop
• Journal of Electrical Engineering and Technology
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• v.8 no.4
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• pp.780-786
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• 2013
• In the reliability-based design optimization of electromagnetic devices, the accurate and efficient reliability assessment method is very essential. The first-order sensitivity-assisted Monte Carlo Simulation is proposed in the former research. In order to improve its accuracy for wide application, in this paper, the second-order sensitivity analysis is presented by using the hybrid direct differentiation-adjoint variable method incorporated with the finite element method. By combining the second-order sensitivity with the Monte Carlo Simulation method, the second-order sensitivity-assisted Monte Carlo Simulation algorithm is proposed to implement reliability calculation. Through application to one superconductor magnetic energy storage system, its accuracy is validated by comparing calculation results with other methods.

### A top-down iteration algorithm for Monte Carlo method for probability estimation of a fault tree with circular logic

• Han, Sang Hoon
• Nuclear Engineering and Technology
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• v.50 no.6
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• pp.854-859
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• 2018
• Calculating minimal cut sets is a typical quantification method used to evaluate the top event probability for a fault tree. If minimal cut sets cannot be calculated or if the accuracy of the quantification result is in doubt, the Monte Carlo method can provide an alternative for fault tree quantification. The Monte Carlo method for fault tree quantification tends to take a long time because it repeats the calculation for a large number of samples. Herein, proposal is made to improve the quantification algorithm of a fault tree with circular logic. We developed a top-down iteration algorithm that combines the characteristics of the top-down approach and the iteration approach, thereby reducing the computation time of the Monte Carlo method.