ABSTRACT As quantitative techniques have become commonplace in the investment industry, the mitig... more ABSTRACT As quantitative techniques have become commonplace in the investment industry, the mitigation of estimation and model risk in portfolio management has grown in importance. Robust optimization, which incorporates estimation error directly into the portfolio optimization process, is typically used with conventional robust statistical estimation methods. This perspective on the robust optimization approach reviews useful practical extensions and discusses potential applications for robust portfolio optimization.
ABSTRACT An overview intended as a short introduction to BLACS, PBLAS, PESSL and ScaLAPACK on the... more ABSTRACT An overview intended as a short introduction to BLACS, PBLAS, PESSL and ScaLAPACK on the IBM SP "Strindberg" at PDC, KTH is given. The major design issues behind the libraries are briefly discussed. Timings and performance measurements are provided for selected subroutines. Some recommendations and hints for better and more efficient usage are given. Key words: BLACS, PBLAS, PESSL, ScaLAPACK, high performance computing, parallel computing, IBM RS/6000 1 Introduction Efficient numerical subroutine libraries are an important part of the infrastructure of high performance scientific computing. They serve as design tools and building blocks for researchers, engineers and developers in many different areas. They provide the non-expert with high efficiency and improved robustness by built-in "state-of the art" knowledge. Today, many numerical libraries have become "de facto" standards in the computing community and hardware vendors are encouraged to provide their own machine specific...
Http Dx Doi Org 10 1080 14697688 2012 664931, Mar 22, 2012
We find a novel correlation structure in the residual noise of stock market returns that is remar... more We find a novel correlation structure in the residual noise of stock market returns that is remarkably linked to the composition and stability of the top few significant factors driving the returns, and moreover indicates that the noise band is composed of multiple subbands that do not fully mix. Our findings allow us to construct effective generalized random matrix theory market models that are closely related to correlation and eigenvector clustering . We show how to use these models in a simulation that incorporates heavy tails. Finally, we demonstrate how a subtle purely stationary risk estimation bias can arise in the conventional cleaning prescription .
Charge and dipole distributions on smooth curves are studied in detail in classical potential the... more Charge and dipole distributions on smooth curves are studied in detail in classical potential theory and have for many years been used as a tool for the numerical solution of boundary value problems of the Laplace equation in two dimensions. Potentials of such distributions are described by simple Redholm integral operators, i.e. the sum of an integral operator with a smooth kernel and a diagonal operator. More recently, techniques have been developed in computational potential theory (in particular, for the Helmholtz equation and related problems involving frequency-domain Maxwell's equations) that replace classical integral equations with combined integro-pseudo-differential equations. This development involves the theory of pseudo-differential operators and has led to an increased interest in the numerical treatment of the latter. In the first part of this dissertation, we present an analysis of all pseudo-differential operators of order up to two encountered in potential theory in two dimensions. In particular, we investigate in detail the analytical structure of pseudo-differential operators converting the densities of charge, dipole, quadrupole, and octapole distributions into their potentials, as well as into the normal, second normal, and third normal derivatives of their potentials on a curve in two dimensions. It turns out that each of these operators is a sum of a standard pseudo-differential operator (derivative, Hilbert transform, derivative of Hilbert transform, and/or the second derivative), an integral operator with smooth kernel, and a diagonal operator. This classification leads to an extremely simple analysis of the spectra of such operators, and simplifies the design of procedures for their numerical evaluation. In the second part of this thesis, we design high-order quadrature formulae for singular and hypersingular integrals for the numerical evaluation of certain pseudo- differential operators. The additional advantage of the scheme is the fact that each of the quadratures it produces can be used simultaneously for the efficient evaluation of hypersingular integrals, Hilbert transforms, and integrals involving both smooth and logarithmically singular functions, which results in significantly simplified implementations. The performance of the procedure is illustrated with several numerical examples.
... TECHREPORT{Kolm95generalizedsubspace, author = {Petter Kolm and Peter ... 8, A direct project... more ... TECHREPORT{Kolm95generalizedsubspace, author = {Petter Kolm and Peter ... 8, A direct projection method for sparse linear systems BENZI, MEYER - 1995. 7, A parallel block projection method of the Cimmino type for finite Markov chains Benzi, Sgallari, et al. - 1995. ...
Se trata de una revisión con un nuevo enfoque de un portafolio de acciones con un modelo financie... more Se trata de una revisión con un nuevo enfoque de un portafolio de acciones con un modelo financiero para el mercado de valores. Los modelos de abordan con rigor matemático y presenta evidencias con diversos ejemplos reales y simulaciones prácticas. Muestra también todos los enfoques principales para el análisis de retorno de un solo periodo, incluida la modelización, estimación y los problemas de optimización. Abarca tanto modelos de análisis de factores estáticos y dinámicos, de cambios de régimen a largo plazo y de cointegración.
As the use of predictive models and optimization techniques have become widespread among portfoli... more As the use of predictive models and optimization techniques have become widespread among portfolio managers, the issue of the confidence practitioners can have in theoretical models has grown in importance. Consequently, there has been an increased level of interest in the subject of robust estimation of parameters and robust optimization of portfolio management models. For years, robustness has been a
... Investment Performance Measurement by Bruce J. Feibel The Handbook of Equity Style Management... more ... Investment Performance Measurement by Bruce J. Feibel The Handbook of Equity Style Management edited by T. Daniel Coggin and Frank J ... Pamela P. Peterson and Frank J. Fabozzi Collateralized Debt Obligations: Structures and Analysis, Second Edition by Douglas J. Lucas ...
ABSTRACT As quantitative techniques have become commonplace in the investment industry, the mitig... more ABSTRACT As quantitative techniques have become commonplace in the investment industry, the mitigation of estimation and model risk in portfolio management has grown in importance. Robust optimization, which incorporates estimation error directly into the portfolio optimization process, is typically used with conventional robust statistical estimation methods. This perspective on the robust optimization approach reviews useful practical extensions and discusses potential applications for robust portfolio optimization.
ABSTRACT An overview intended as a short introduction to BLACS, PBLAS, PESSL and ScaLAPACK on the... more ABSTRACT An overview intended as a short introduction to BLACS, PBLAS, PESSL and ScaLAPACK on the IBM SP "Strindberg" at PDC, KTH is given. The major design issues behind the libraries are briefly discussed. Timings and performance measurements are provided for selected subroutines. Some recommendations and hints for better and more efficient usage are given. Key words: BLACS, PBLAS, PESSL, ScaLAPACK, high performance computing, parallel computing, IBM RS/6000 1 Introduction Efficient numerical subroutine libraries are an important part of the infrastructure of high performance scientific computing. They serve as design tools and building blocks for researchers, engineers and developers in many different areas. They provide the non-expert with high efficiency and improved robustness by built-in "state-of the art" knowledge. Today, many numerical libraries have become "de facto" standards in the computing community and hardware vendors are encouraged to provide their own machine specific...
Http Dx Doi Org 10 1080 14697688 2012 664931, Mar 22, 2012
We find a novel correlation structure in the residual noise of stock market returns that is remar... more We find a novel correlation structure in the residual noise of stock market returns that is remarkably linked to the composition and stability of the top few significant factors driving the returns, and moreover indicates that the noise band is composed of multiple subbands that do not fully mix. Our findings allow us to construct effective generalized random matrix theory market models that are closely related to correlation and eigenvector clustering . We show how to use these models in a simulation that incorporates heavy tails. Finally, we demonstrate how a subtle purely stationary risk estimation bias can arise in the conventional cleaning prescription .
Charge and dipole distributions on smooth curves are studied in detail in classical potential the... more Charge and dipole distributions on smooth curves are studied in detail in classical potential theory and have for many years been used as a tool for the numerical solution of boundary value problems of the Laplace equation in two dimensions. Potentials of such distributions are described by simple Redholm integral operators, i.e. the sum of an integral operator with a smooth kernel and a diagonal operator. More recently, techniques have been developed in computational potential theory (in particular, for the Helmholtz equation and related problems involving frequency-domain Maxwell's equations) that replace classical integral equations with combined integro-pseudo-differential equations. This development involves the theory of pseudo-differential operators and has led to an increased interest in the numerical treatment of the latter. In the first part of this dissertation, we present an analysis of all pseudo-differential operators of order up to two encountered in potential theory in two dimensions. In particular, we investigate in detail the analytical structure of pseudo-differential operators converting the densities of charge, dipole, quadrupole, and octapole distributions into their potentials, as well as into the normal, second normal, and third normal derivatives of their potentials on a curve in two dimensions. It turns out that each of these operators is a sum of a standard pseudo-differential operator (derivative, Hilbert transform, derivative of Hilbert transform, and/or the second derivative), an integral operator with smooth kernel, and a diagonal operator. This classification leads to an extremely simple analysis of the spectra of such operators, and simplifies the design of procedures for their numerical evaluation. In the second part of this thesis, we design high-order quadrature formulae for singular and hypersingular integrals for the numerical evaluation of certain pseudo- differential operators. The additional advantage of the scheme is the fact that each of the quadratures it produces can be used simultaneously for the efficient evaluation of hypersingular integrals, Hilbert transforms, and integrals involving both smooth and logarithmically singular functions, which results in significantly simplified implementations. The performance of the procedure is illustrated with several numerical examples.
... TECHREPORT{Kolm95generalizedsubspace, author = {Petter Kolm and Peter ... 8, A direct project... more ... TECHREPORT{Kolm95generalizedsubspace, author = {Petter Kolm and Peter ... 8, A direct projection method for sparse linear systems BENZI, MEYER - 1995. 7, A parallel block projection method of the Cimmino type for finite Markov chains Benzi, Sgallari, et al. - 1995. ...
Se trata de una revisión con un nuevo enfoque de un portafolio de acciones con un modelo financie... more Se trata de una revisión con un nuevo enfoque de un portafolio de acciones con un modelo financiero para el mercado de valores. Los modelos de abordan con rigor matemático y presenta evidencias con diversos ejemplos reales y simulaciones prácticas. Muestra también todos los enfoques principales para el análisis de retorno de un solo periodo, incluida la modelización, estimación y los problemas de optimización. Abarca tanto modelos de análisis de factores estáticos y dinámicos, de cambios de régimen a largo plazo y de cointegración.
As the use of predictive models and optimization techniques have become widespread among portfoli... more As the use of predictive models and optimization techniques have become widespread among portfolio managers, the issue of the confidence practitioners can have in theoretical models has grown in importance. Consequently, there has been an increased level of interest in the subject of robust estimation of parameters and robust optimization of portfolio management models. For years, robustness has been a
... Investment Performance Measurement by Bruce J. Feibel The Handbook of Equity Style Management... more ... Investment Performance Measurement by Bruce J. Feibel The Handbook of Equity Style Management edited by T. Daniel Coggin and Frank J ... Pamela P. Peterson and Frank J. Fabozzi Collateralized Debt Obligations: Structures and Analysis, Second Edition by Douglas J. Lucas ...
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