We price continuously monitored barrier options under GBM and SABR through a newly developed neural network, the COS-CPD network, based on the COS-CPD method. With the pricing PDE and the COS method, we transform the problem of pricing the barrier options into a problem of finding the survival characteristic function through an initial boundary value problem. By applying trigonometric expansion, derived by integrating out the Fourier expansion on the time derivative of the unknown function, to the survival characteristic function, we find an approximation that can be inserted into the IBVP. Without CPD, this results in a linear system which can be solved to find the expansion coefficients, but this leads to the curse of dimensionality. If we include CPD to remove this curse of dimensionality, resulting in the COS-CPD network, the Alternating Least Squares method must be used to find the factor matrices that replace the original expansion coefficient tensor.

Due to human advancement in recent centuries, extinction rates of animals and plants around the earth have greatly risen. Conservation biology, the study of conservation of nature and earth’s biodiversity, aims to protect species from these increasing extinction rates.
Phylogenetic diversity is a measure for biodiversity that can help in selecting which species to prioritize in preserving diversity. This is necessary because there are bounds on how many of these species can be preserved, due to costs connected to this preservation. To aid in selecting the subset of species with maximum diversity, an ILP can be formulated to find this subset. In this thesis these ILP’s will be formulated for different phylogenetic networks and functions that give a diversity score to these subsets.