Green Bond Valuation: A Numerical Mathematics Perspective: Assessing the Influence of Environmental Factors

This thesis presents a novel approach to the pricing of green bonds, a growing segment in financial markets with an emphasis on environmental sustainability. Unlike traditional financial instruments, green bonds uniquely incorporate environmental considerations, particularly carbon price (c_t), along with traditional factors like the short rate ...

On the Convergence Behavior of IDR(s) and Related Methods

An explanation is given of the convergence behavior of IDR(s) methods. The convergence mechanism of these algorithms has two components. The first consists of damping properties of certain factors in the residual polynomials, which becomes less important for large values of s. The second component depends on the behavior of Lanczos polynomials...

Exploiting BiCGstab(?) strategies to induce dimension reduction

IDR(s) [P. Sonneveld and M. B. van Gijzen, SIAM J. Sci. Comput., 31 (2008), pp. 1035–1062] and BiCGstab(?) [G. L. G. Sleijpen and D. R. Fokkema, Electron. Trans. Numer. Anal., 1 (1993), pp. 11–32] are two of the most efficient short-recurrence iterative methods for solving large nonsymmetric linear systems of equations. Which of the two is best...

On the convergence behaviour of IDR(s)

An explanation is given of the convergence behaviour of the IDR(s) methods. The convergence of the IDR(s) algorithms has two components. The first consists of damping properties of certain factors in the residual polynomials, which becomes less important for large values of s. The second component depends on the behaviour of quasi-Lanczos...

A preconditioner for the Helmholtz equation with perfectly matched layer

This paper discusses an iterative method for solving the Helmholtz equation with the perfectly matched layer (PML). The method consists of an outer and inner iteration process. The inner iteration is used to approximately solve a preconditioner, which in this case is based on a modified PML equation. The outer iteration is a Krylov subspace...

On a class of preconditioners for solving the Helmholtz equation