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2 Annals of Computer Science and Information Systems

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An Optimized Stochastic Techniques related to Option Pricing

Todorov Venelin, Dimov Ivan, Fidanova Stefka, Apostolov Stoyan

Annals of Computer Science and Information Systems

2021

Vol. 25

247--250

Recently stochastic methods have become very important tool for high performance computing of very high dimensional problems in computational finance. The advantages and disadvantages of the different highly efficient stochastic methods for multidimensional integrals related to evaluation of European style options will be analyzed. Multidimensional integrals up to 100 dimensions related to European options will be computed with highly efficient optimized lattice rules.

A New Optimized Stochastic Approach for Multidimensional Integrals in Machine Learning

Todorov Venelin, Apostolov Stoyan, Dimov Ivan, Fidanova Stefka

Annals of Computer Science and Information Systems

2020

Vol. 21

337--340

Stochastic techniques have been developed over many years in a range of different fields, but have only recently been applied to the problems in machine learning. A fundamental problem in this area is the accurate evaluation of multidimensional integrals. An introduction to the theory of the stochastic optimal generating vectors has been given. A new optimized lattice sequence with a special choice of the optimal generating vector have been applied to compute multidimensional integrals up to 30-dimensions. Clearly, the progress in the area of machine learning is closely related to the progress in reliable algorithms for multidimensional integration.