QUASI-MONTE CARLO METHODS BASED ON SOBOL AND HALTON SEQUENCES FOR COMPUTATION OF MULTIDIMENSIONAL INTEGRALS APPLIED IN SECURITY SYSTEMS
QUASI-MONTE CARLO METHODS BASED ON SOBOL AND HALTON SEQUENCES FOR COMPUTATION OF MULTIDIMENSIONAL INTEGRALS APPLIED IN SECURITY SYSTEMS
DOI:
https://doi.org/10.46687/jsar.v16i1.259Keywords:
Financial mathematics, Quasi-Monte Carlo algorithms, multidimensional integrals, Halton sequence, Sobol sequence, Computational complexityAbstract
In this paper we implement and analyze the performance of Sobol quasi-random sequence and compare the results with the Halton quasi-random sequence has been done. We consider a case study with a non-smooth integrand function with applications in financial mathematics. We show that the Sobol sequence has some advantageous over the Halton sequence. It is established that Sobol sequence performs bett er than other sequences for higher dimensions.
Author Biographies
Venelin Todorov, Bulgarian Academy of Sciences, Institute of Mathematics and Informatics and Institute of Inormation and Communication Technologies: Sofia, BG
Bulgarian Academy of Sciences, Institute of Mathematics and Informatics and Institute of Inormation and Communication Technologies: Sofia, BG
https://orcid.org/0000-0001-7134-5901Iliyan Tsvetkov, ROUSSE UNIVERSITY ”ANGEL KANCHEV”
ROUSSE UNIVERSITY ”ANGEL KANCHEV”
Tosho Stanchev, ROUSSE UNIVERSITY ”ANGEL KANCHEV”
ROUSSE UNIVERSITY ”ANGEL KANCHEV”
Yuri Dimitrov, UNIVERSITY OF FORESTRY, SOFIA, DEPARTMENT OF MATHEMATICS AND PHYSICS
UNIVERSITY OF FORESTRY, SOFIA, DEPARTMENT OF MATHEMATICS AND PHYSICS
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