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The aim of this thesis is to investigate a neural network-like approach for the numerical solution of a class of fractional PDEs, and in particular the space fractional Black–Scholes equation for pricing European options, which has been recently considered in  by using a finite difference scheme.
 V. Dwivedi, B. Srinivasan, Physics Informed Extreme Learning Machine (PIELM)–A rapid method for the numerical solution of partial differential equations, Neurocomputing 391 (2020) 96–118
 Q. Wei, Y. Jiang, J. Z. Y. Chen, Machine-learning solver for modified diffusion equations, PHYSICAL REVIEW E 98 (2018) 053304
 H. Qu, Z. She, X. Liu, Neural network method for solving fractional diffusion equations, Applied Mathematics and Computation 391 (2021) 125635
 K. S. Patel , M. Mehra, Fourth order compact scheme for space fractional advection–diffusion reaction equations with variable coefficients, Journal of Computational and Applied Mathematics 380 (2020) 112963
 M. Raissi, G. E.Karniadakis, Hidden physics models: Machine learning of nonlinear partial differential equations, J. Comput. Phys. 357 (2018) 125–14
The aim of this thesis is to discuss a comparison among different metaheuristics (i.e. population-based and non-population-based algorithms) by considering the latest algorithms, such as the String Theory Algorithm (STA) . STA is a nature-inspired meta-heuristic, based on a theory from modern physics (i.e. String Theory), where the elemental objects are strings, whose vibrations determine the particles properties. Some benchmark datasets will be considered for the comparative purposes (e.g. ).
 A. Soler-Dominguez, A. A. Juan, R. Kizys, 1A Survey on Financial Applications of Metaheuristics, ACM Computing Surveys, 50(1), 15:1-19, 2017.
 M. Dhaini, N. Mansour, Squirrel search algorithm for portfolio optimization, Expert Systems With Applications, 178, 114968, 2021.
 T. E. Simos, S. D. Mourtas, V. N. Katsikis, Time-varying Black–Litterman portfolio optimization using a bio-inspired approach and neuronets, Applied Soft Computing, 112, 107767, 2021
 L. Rodriguez, O. Castillo, M. Garcia, J. Soria, A new meta-heuristic optimization algorithm based on a paradigm from physics: string theory, Journal of Intelligent & Fuzzy Systems, 41 (1) 1657-1675, 2021
One assumption to find the price of option is the assumption of the behavior of the underlying asset (eg share) price. In the most common case, it is assumed that the price of the underlying asset behaves according to the geometric Brown movement in which the volatility of the underlying asset is constant. However, this assumption may not be valid in practice and volatility behavior can often be described as a random process. The master's thesis is intended to provide an overview of option valuation in case of stochastic volatility. Various numerical methods based on the binomial method proposed in the literature are examined in more detail. It is planned to draw up the corresponding program and carry out numerical experiments.
The student interested in the topic will analyze a real data set with the purpose to evaluate and compare different classification methods. The proper use of dichotomous and nominal input variables will be of special interest in this work.
7. Overview and simulation study of performance of extensions of kNN, supervisor Raul Kangro