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Fractional Brownian motion and the Markov property
 Cvitanic J., Lazrak A., Martellini L., and Zapatero F., Revisiting Treynor and Black
, 1998
"... Abstract. Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This leads naturaly to: • An efficient algorithm to approximate the process. • An ergodic theorem which applies to functi ..."
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Cited by 4 (0 self)
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Abstract. Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This leads naturaly to: • An efficient algorithm to approximate the process. • An ergodic theorem which applies to functionals of the type ∫ t ∫ t φ(Vh(s))ds where Vh(s) = h(t − u)dBu. 0 1.
INVERTIBILITY OF THE GABOR FRAME OPERATOR ON THE WIENER AMALGAM SPACE
, 705
"... Abstract. We use a generalization of Wiener’s 1/f theorem to prove that for a Gabor frame with the generator in the Wiener amalgam space W (L ∞ , ℓ 1)(R d), the corresponding frame operator is invertible on this space. Therefore, for such a Gabor frame, the generator of the canonical dual belongs al ..."
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Cited by 3 (1 self)
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Abstract. We use a generalization of Wiener’s 1/f theorem to prove that for a Gabor frame with the generator in the Wiener amalgam space W (L ∞ , ℓ 1)(R d), the corresponding frame operator is invertible on this space. Therefore, for such a Gabor frame, the generator of the canonical dual belongs also to W (L ∞ , ℓ 1)(R d). 1.
Optimal Investment with an Unbounded Random Endowment and UtilityBased Pricing
, 706
"... This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the existence of an optimal trading strategy within a class of permiss ..."
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This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the existence of an optimal trading strategy within a class of permissible strategies – those strategies whose wealth process is a supermartingale under all pricing measures with finite relative entropy. We give necessary and sufficient conditions for the absence of utilitybased arbitrage, and for the existence of a solution to the primal problem. We consider two utilitybased methods which can be used to price contingent claims. Firstly we investigate marginal utilitybased price processes (MUBPP’s). We show that such processes can be characterized as local martingales under the normalized optimal dual measure for the utility maximizing investor. Finally, we present some new results on utility indifference prices, including continuity properties and volume asymptotics for the case of a general utility function, unbounded endowment and unbounded contingent claims. 1
ELECTRONIC COMMUNICATIONS in PROBABILITY FRACTIONAL BROWNIAN MOTION AND THE MARKOV PROPERTY
, 1997
"... Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This leads naturally to: • An efficient algorithm to approximate the process. • An ergodic theorem which applies to functionals of ..."
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Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This leads naturally to: • An efficient algorithm to approximate the process. • An ergodic theorem which applies to functionals of the type ∫ t 0 φ(Vh(s)) ds where Vh(s) = ∫ s 0 h(s − u) dBu. and B is a real Brownian motion. 1
missions of CIRANO: to develop the scientific analysis of organizations and strategic behaviour. Les organisationspartenaires / The Partner Organizations
"... Le CIRANO est un organisme sans but lucratif constitué en vertu de la Loi des compagnies du Québec. Le financement de son infrastructure et de ses activités de recherche provient des cotisations de ses organisationsmembres, d=une subvention d=infrastructure du ministère de l=Industrie, du Commerce, ..."
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Le CIRANO est un organisme sans but lucratif constitué en vertu de la Loi des compagnies du Québec. Le financement de son infrastructure et de ses activités de recherche provient des cotisations de ses organisationsmembres, d=une subvention d=infrastructure du ministère de l=Industrie, du Commerce, de la Science et de la Technologie, de même que des subventions et mandats obtenus par ses équipes de recherche. La Série Scientifique est la réalisation d=une des missions que s=est données le CIRANO, soit de développer l=analyse scientifique des organisations et des comportements stratégiques. CIRANO is a private nonprofit organization incorporated under the Québec Companies Act. Its infrastructure and research activities are funded through fees paid by member organizations, an infrastructure grant from the Ministère de l=Industrie, du Commerce, de la Science et de la Technologie, and grants and research mandates obtained by its research teams. The Scientific Series fulfils one of the
Linear Algebra and Analysis
, 2007
"... The purpose of this first set of lecture notes is to summarize background material on linear algebra and analysis that is used throughout the course. Proofs of most of the stated facts may be found in the references listed at the end of the notes. It is my intention that this first set of notes will ..."
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The purpose of this first set of lecture notes is to summarize background material on linear algebra and analysis that is used throughout the course. Proofs of most of the stated facts may be found in the references listed at the end of the notes. It is my intention that this first set of notes will mostly serve as a useful reference later in the course. 1 LINEAR ALGEBRA The theory of quantum information is based on linear algebra, and in particular the study of finite dimensional vector spaces over the real or complex numbers. We will mostly focus on complex vector spaces, but sometimes it will be necessary to work with real vector spaces. Vector spaces over the real or complex numbers will be denoted by scripted capital letters in this course, generally near the end of the alphabet such as X, Y, and Z. Elements of these spaces will be denoted by lowercase Roman letters such as u, v, w and x. Subsets of vector spaces, which may not themselves be vector spaces, will also be denoted by scripted letters, usually near the beginning of the alphabet such as A, B, and C. The field of real numbers is denoted R and the field of complex numbers is denoted C. 1.1 INNER PRODUCTS, NORMS, AND COMPLEX EUCLIDEAN SPACES
A MODIFIED QUASIREVERSIBILITY METHOD FOR A CLASS OF ILLPOSED CAUCHY PROBLEMS
"... Abstract. The goal of this paper is to present some extensions of the method of quasireversibility applied to an illposed Cauchy problem associated with an unbounded linear operator in a Hilbert space. The key point to our proof is the use of a new perturbation to construct a family of regularizin ..."
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Abstract. The goal of this paper is to present some extensions of the method of quasireversibility applied to an illposed Cauchy problem associated with an unbounded linear operator in a Hilbert space. The key point to our proof is the use of a new perturbation to construct a family of regularizing operators for the considered problem. We show the convergence of this method, and we estimate the convergence rate under a priori regularity assumptions on the problem data.
Some criteria for determining when a Walsh Series is a WalshFourier Series
, 2002
"... We show that a general Walsh series is the WalshFourier series of a function f ∈ Lp[0, 1] for 1 ≤ p < ∞ if and only if its sequence of partial sums contains a relatively weakly compact subsequence. Several other criteria are established for the case where f ∈ LΦ[0, 1], the Orlicz space generated ..."
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We show that a general Walsh series is the WalshFourier series of a function f ∈ Lp[0, 1] for 1 ≤ p < ∞ if and only if its sequence of partial sums contains a relatively weakly compact subsequence. Several other criteria are established for the case where f ∈ LΦ[0, 1], the Orlicz space generated by an Nfunction Φ.