Exact Smooth Term Structure Estimation

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In this thesis we will present and analyze randomized algorithms for numerical linear algebra problems. An important theme in this thesis is randomized low-rank approximation. In particular, we will study randomized low-rank approximation of matrix functio ...

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

In this thesis we present three closed form approximation methods for portfolio valuation and risk management. The first chapter is titled ``Kernel methods for portfolio valuation and risk management'', and is a joint work with Damir Filipovi'c (SFI and ...

Using data on international equity portfolio allocations by U.S. mutual funds, we estimate a portfolio expression derived from a standard mean-variance portfolio model extended with portfolio frictions. The optimal portfolio depends on the previous month a ...

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model ...

This thesis uses machine learning techniques and text data to investigate the relationships that arise between the Fed and financial markets, and their consequences for asset prices. The first chapter, entitled Market Expectations and the Impact of Unconv ...

This thesis focuses on non-parametric covariance estimation for random surfaces, i.e.~functional data on a two-dimensional domain. Non-parametric covariance estimation lies at the heart of functional data analysis, and considerations of statistical and com ...

We consider a least-squares/relaxation finite element method for the numerical solution of the prescribed Jacobian equation. We look for its solution via a least-squares approach. We introduce a relaxation algorithm that decouples this least-squares proble ...

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector corresponding to the smal ...

Kernel methods are fundamental tools in machine learning that allow detection of non-linear dependencies between data without explicitly constructing feature vectors in high dimensional spaces. A major disadvantage of kernel methods is their poor scalabili ...

This thesis focuses on developing efficient algorithmic tools for processing large datasets. In many modern data analysis tasks, the sheer volume of available datasets far outstrips our abilities to process them. This scenario commonly arises in tasks incl ...

This thesis studies the valuation and hedging of financial derivatives, which is fundamental for trading and risk-management operations in financial institutions. The three chapters in this thesis deal with derivatives whose payoffs are linked to interest ...

We present a nonparametric method to estimate the discount curve from market quotes based on the Moore-Penrose pseudoinverse. The discount curve reproduces the market quotes perfectly, has maximal smoothness, and is given in closed-form. The method is easy ...

The multiquery solution of parametric partial differential equations (PDEs), that is, PDEs depending on a vector of parameters, is computationally challenging and appears in several engineering contexts, such as PDE-constrained optimization, uncertainty qu ...

We introduce the class of linear-rational term structure models in which the state price density is modeled such that bond prices become linear-rational functions of the factors. This class is highly tractable with several distinct advantages: (i) ensures ...

This thesis contains four chapters, each of which utilizes new or unusual data sources to analyze a different area of financial economics. In the first chapter, I construct a novel dataset linking individual bankers to large borrowers in the U.S. syndicate ...

With the advent of emerging technologies and the Internet of Things, the importance of online data analytics has become more pronounced. Businesses and companies are adopting approaches that provide responsive analytics to stay competitive in the global ma ...

Traditional approaches to analysing functional data typically follow a two-step procedure, consisting in first smoothing and then carrying out a functional principal component analysis. The idea underlying this procedure is that functional data are well ap ...

In this thesis, we present a Riemannian framework for the solution of high-dimensional optimization problems with an underlying low-rank tensor structure. Here, the high-dimensionality refers to the size of the search space, while the cost function is scal ...

Exact Smooth Term Structure Estimation

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Randomized low-rank approximation and its applications

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Closed form approximation methods for portfolio valuation and risk management

International Portfolio Choice with Frictions: Evidence from Mutual Funds

TimeEvolver: A program for time evolution with improved error bound

Connecting Hodge and Sakaguchi-Kuramoto through a mathematical framework for coupled oscillators on simplicial complexes

Essays in Monetary Policy and Asset Pricing

Covariance Estimation for Random Surfaces beyond Separability

A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation

Eigendecomposition-Free Training of Deep Networks for Linear Least-Square Problems

Oblivious Sketching of High-Degree Polynomial Kernels

Fourier Sampling in Signal Processing and Numerical Linear Algebra

Pricing interest rate, dividend, and equity risk

Exact Smooth Term-Structure Estimation

Multi space reduced basis preconditioners for parametrized partial differential equations

Linear-Rational Term Structure Models

Essays in Financial Economics

Efficient Online Processing for Advanced Analytics

Functional data analysis by matrix completion

Riemannian Optimization for Solving High-Dimensional Problems with Low-Rank Tensor Structure