scholarly journals HARGA OPSI CALL TIPE EROPA MENGGUNAKAN SIMULASI MONTE CARLO STANDAR DAN TEKNIK ANTITHETIC VARIATES

2020 ◽  
Vol 8 (2) ◽  
pp. 7
Author(s):  
Anisah Mardiah Qur’ani ◽  
Irwan Kasse ◽  
Ilham Syata
Keyword(s):  
Monte Carlo ◽  
Antithetic Variates

scholarly journals On spherical Monte Carlo simulations for multivariate normal probabilities

2015 ◽  
Vol 47 (03) ◽  
pp. 817-836 ◽  
Author(s):  
Huei-Wen Teng ◽  
Ming-Hsuan Kang ◽  
Cheng-Der Fuh
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Variance Reduction ◽  
Multivariate Normal ◽  
Integration Rule ◽  
Radial Integral ◽  
Normal Probability ◽  
Antithetic Variates ◽  
Number Problem ◽  
Spherical Transformation

The calculation of multivariate normal probabilities is of great importance in many statistical and economic applications. In this paper we propose a spherical Monte Carlo method with both theoretical analysis and numerical simulation. We start by writing the multivariate normal probability via an inner radial integral and an outer spherical integral using the spherical transformation. For the outer spherical integral, we apply an integration rule by randomly rotating a predetermined set of well-located points. To find the desired set, we derive an upper bound for the variance of the Monte Carlo estimator and propose a set which is related to the kissing number problem in sphere packings. For the inner radial integral, we employ the idea of antithetic variates and identify certain conditions so that variance reduction is guaranteed. Extensive Monte Carlo simulations on some probabilities confirm these claims.

General principles of antithetic variates

1956 ◽  
Vol 52 (3) ◽  
pp. 476-481 ◽  
Author(s):  
J. M. Hammersley ◽  
J. G. Mauldon
Keyword(s):  
Monte Carlo ◽  
Theoretical Structure ◽  
Antithetic Variates

1. In (2) the idea of antithetic variates in Monte Carlo work is introduced and applied to the estimation of integrals. The present paper studies the general theoretical structure of antithetic variates. We have made only limited progress and present various unsolved problems as a challenge to the reader.

scholarly journals On spherical Monte Carlo simulations for multivariate normal probabilities

2015 ◽  
Vol 47 (3) ◽  
pp. 817-836 ◽  
Author(s):  
Huei-Wen Teng ◽  
Ming-Hsuan Kang ◽  
Cheng-Der Fuh
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Variance Reduction ◽  
Multivariate Normal ◽  
Integration Rule ◽  
Radial Integral ◽  
Normal Probability ◽  
Antithetic Variates ◽  
Number Problem ◽  
Spherical Transformation

The calculation of multivariate normal probabilities is of great importance in many statistical and economic applications. In this paper we propose a spherical Monte Carlo method with both theoretical analysis and numerical simulation. We start by writing the multivariate normal probability via an inner radial integral and an outer spherical integral using the spherical transformation. For the outer spherical integral, we apply an integration rule by randomly rotating a predetermined set of well-located points. To find the desired set, we derive an upper bound for the variance of the Monte Carlo estimator and propose a set which is related to the kissing number problem in sphere packings. For the inner radial integral, we employ the idea of antithetic variates and identify certain conditions so that variance reduction is guaranteed. Extensive Monte Carlo simulations on some probabilities confirm these claims.

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