Abstract
In this work we study advanced stochastic methods for solving a specific multidimensional problems related to computation of European style options in computational finance. Recently, stochastic methods have become a very important tool for high-performance computing of very high-dimensional problems in computational finance. Here, a different kind of optimal generating vectors have been applied for the first time to a specific problem in computational finance. Numerical tests show that they give superior results to the stochastic approaches used up to now. The advantages and disadvantages of various highly efficient stochastic approaches for multidimensional integrals related to evaluation of European style options have been analyzed.
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Acknowledgment
Venelin Todorov is supported by the Bulgarian National Science Fund under the Project KP-06-N52/5 “Efficient methods for modeling, optimization and decision making” and Project KP-06-N52/2 “Perspective Methods for Quality Prediction in the Next Generation Smart Informational Service Networks”. Stoyan Apostolov is supported by the Bulgarian National Science Fund under Project KP-06-M32/2 - 17.12.2019 “Advanced Stochastic and Deterministic Approaches for Large-Scale Problems of Computational Mathematics”. The work is also supported by the NSP “ICT in SES”, contract No DO1-205/23.11.2018, financed by the Ministry of EU in Bulgaria and by the BNSF under Project KP-06-Russia/17 “New Highly Efficient Stochastic Simulation Methods and Applications” and Project DN 12/4-2017 “Advanced Analytical and Numerical Methods for Nonlinear Differential Equations with Applications in Finance and Environmental Pollution”.
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Todorov, V., Dimov, I., Georgieva, R., Apostolov, S., Poryazov, S. (2022). Advanced Stochastic Approaches Based on Optimization of Lattice Sequences for Large-Scale Finance Problems. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2021. Lecture Notes in Computer Science, vol 13127. Springer, Cham. https://doi.org/10.1007/978-3-030-97549-4_30
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DOI: https://doi.org/10.1007/978-3-030-97549-4_30
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