A geometric point of view on mean-variance models

Piotr Jaworski

Displaying similar documents to “A geometric point of view on mean-variance models”

Existentially closed II₁ factors

Ilijas Farah, Isaac Goldbring, Bradd Hart, David Sherman (2016)

Fundamenta Mathematicae

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We examine the properties of existentially closed ( $^{ω}$ -embeddable) II₁ factors. In particular, we use the fact that every automorphism of an existentially closed ( $^{ω}$ -embeddable) II₁ factor is approximately inner to prove that Th() is not model-complete. We also show that Th() is complete for both finite and infinite forcing and use the latter result to prove that there exist continuum many nonisomorphic existentially closed models of Th().

On the structure of the set of higher order spreading models

Bünyamin Sarı, Konstantinos Tyros (2014)

Studia Mathematica

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We generalize some results concerning the classical notion of a spreading model to spreading models of order ξ. Among other results, we prove that the set $S M_{ξ}^{w} (X)$ of ξ-order spreading models of a Banach space X generated by subordinated weakly null ℱ-sequences endowed with the pre-partial order of domination is a semilattice. Moreover, if $S M_{ξ}^{w} (X)$ contains an increasing sequence of length ω then it contains an increasing sequence of length ω₁. Finally, if $S M_{ξ}^{w} (X)$ is uncountable, then it contains an antichain...

On sets of confluent and related mappings in the space $Y^{X}$

T. Maćkowiak (1976)

Colloquium Mathematicae

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Chaotic behaviour of continuous dynamical system generated by Euler equation branching and its application in macroeconomic equilibrium model

Barbora Volná (2015)

Mathematica Bohemica

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We focus on the special type of the continuous dynamical system which is generated by Euler equation branching. Euler equation branching is a type of differential inclusion $\dot{x} \in {f (x), g (x)}$ , where $f, g : X \subset ℝ^{n} \to ℝ^{n}$ are continuous and $f (x) \neq g (x)$ at every point $x \in X$ . It seems this chaotic behaviour is typical for such dynamical system. In the second part we show an application in a new formulated overall macroeconomic equilibrium model. This new model is based on the fundamental macroeconomic aggregate equilibrium model called...

Stein’s method in high dimensions with applications

Adrian Röllin (2013)

Annales de l'I.H.P. Probabilités et statistiques

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Let $h$ be a three times partially differentiable function on $ℝ^{n}$ , let $X = (X_{1}, ..., X_{n})$ be a collection of real-valued random variables and let $Z = (Z_{1}, ..., Z_{n})$ be a multivariate Gaussian vector. In this article, we develop Stein’s method to give error bounds on the difference $𝔼 h (X) - 𝔼 h (Z)$ in cases where the coordinates of $X$ are not necessarily independent, focusing on the high dimensional case $n \to \infty$ . In order to express the dependency structure we use Stein couplings, which allows for a broad range of applications, such as classic...

Generic extensions of models of ZFC

Lev Bukovský (2017)

Commentationes Mathematicae Universitatis Carolinae

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The paper contains a self-contained alternative proof of my Theorem in Characterization of generic extensions of models of set theory, Fund. Math. 83 (1973), 35–46, saying that for models $M \subseteq N$ of ZFC with same ordinals, the condition $A p r_{M, N} (κ)$ implies that $N$ is a $κ$ -C.C. generic extension of $M$ .

Uniform regularity for an isentropic compressible MHD- $P 1$ approximate model arising in radiation hydrodynamics

Tong Tang, Jianzhu Sun (2021)

Czechoslovak Mathematical Journal

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It is well known that people can derive the radiation MHD model from an MHD- $P 1$ approximate model. As pointed out by F. Xie and C. Klingenberg (2018), the uniform regularity estimates play an important role in the convergence from an MHD- $P 1$ approximate model to the radiation MHD model. The aim of this paper is to prove the uniform regularity of strong solutions to an isentropic compressible MHD- $P 1$ approximate model arising in radiation hydrodynamics. Here we use the bilinear commutator and...

Constructibility in Ackermann's set theory

C. Alkor

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CONTENTSIntroduction......................... 5Section I. Preliminaries............ 6 § 1. Notation..................... 6 § 2. Ackermann’s set theory and some extensions................. 7 § 3. Absoluteness............................................... 8 § 4. Ordinals................................................... 9 § 5. Reflection principles...................................... 10Section 2. The usual notion of constructibility.............. 11 § 1. General considerations about...

Logarithmically improved blow-up criterion for smooth solutions to the Leray- $α$ -magnetohydrodynamic equations

Ines Ben Omrane, Sadek Gala, Jae-Myoung Kim, Maria Alessandra Ragusa (2019)

Archivum Mathematicum

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In this paper, the Cauchy problem for the $3 D$ Leray- $α$ -MHD model is investigated. We obtain the logarithmically improved blow-up criterion of smooth solutions for the Leray- $α$ -MHD model in terms of the magnetic field $B$ only in the framework of homogeneous Besov space with negative index.

The number of $L_{\infty κ}$ -equivalent nonisomorphic models for κ weakly compact

Saharon Shelah, Pauli Vaisanen (2002)

Fundamenta Mathematicae

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For a cardinal κ and a model M of cardinality κ let No(M) denote the number of nonisomorphic models of cardinality κ which are $L_{\infty, κ}$ -equivalent to M. We prove that for κ a weakly compact cardinal, the question of the possible values of No(M) for models M of cardinality κ is equivalent to the question of the possible numbers of equivalence classes of equivalence relations which are Σ¹₁-definable over $V_{κ}$ . By [SV] it is possible to have a generic extension where the possible numbers of equivalence...

Higher order spreading models

S. A. Argyros, V. Kanellopoulos, K. Tyros (2013)

Fundamenta Mathematicae

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We introduce higher order spreading models associated to a Banach space X. Their definition is based on ℱ-sequences ${(x_{s})}_{s \in ℱ}$ with ℱ a regular thin family and on plegma families. We show that the higher order spreading models of a Banach space X form an increasing transfinite hierarchy ${(ℳ_{ξ} (X))}_{ξ < ω ₁}$ . Each $ℳ_{ξ} (X)$ contains all spreading models generated by ℱ-sequences ${(x_{s})}_{s \in ℱ}$ with order of ℱ equal to ξ. We also study the fundamental properties of this hierarchy.

Counting models of set theory

Ali Enayat (2002)

Fundamenta Mathematicae

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Let T denote a completion of ZF. We are interested in the number μ(T) of isomorphism types of countable well-founded models of T. Given any countable order type τ, we are also interested in the number μ(T,τ) of isomorphism types of countable models of T whose ordinals have order type τ. We prove: (1) Suppose ZFC has an uncountable well-founded model and $κ \in ω \cup ℵ ₀, ℵ ₁, 2^{ℵ ₀}$ . There is some completion T of ZF such that μ(T) = κ. (2) If α <ω₁ and μ(T,α) > ℵ₀, then $μ (T, α) = 2^{ℵ ₀}$ . (3) If α < ω₁ and T ⊢ V ≠ OD,...

Odd cutsets and the hard-core model on $ℤ^{d}$

Ron Peled, Wojciech Samotij (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We consider the hard-core lattice gas model on $ℤ^{d}$ and investigate its phase structure in high dimensions. We prove that when the intensity parameter exceeds $C d^{- 1 / 3} {(log d)}^{2}$ , the model exhibits multiple hard-core measures, thus improving the previous bound of $C d^{- 1 / 4} {(log d)}^{3 / 4}$ given by Galvin and Kahn. At the heart of our approach lies the study of a certain class of edge cutsets in $ℤ^{d}$ , the so-called odd cutsets, that appear naturally as the boundary between different phases in the hard-core model. We provide a refined...

Routh-type $L_{2}$ model reduction revisited

Wiesław Krajewski, Umberto Viaro (2018)

Kybernetika

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A computationally simple method for generating reduced-order models that minimise the $L_{2}$ norm of the approximation error while preserving a number of second-order information indices as well as the steady-state value of the step response, is presented. The method exploits the energy-conservation property peculiar to the Routh reduction method and the interpolation property of the $L_{2}$ -optimal approximation. Two examples taken from the relevant literature show that the suggested techniques...

The Brouwer Fixed Point Theorem for Some Set Mappings

Dariusz Miklaszewski (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

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For some classes $X \subset 2^{ₙ}$ of closed subsets of the disc ₙ ⊂ ℝⁿ we prove that every Hausdorff-continuous mapping f: X → X has a fixed point A ∈ X in the sense that the intersection A ∩ f(A) is nonempty.

On the geometry of proportional quotients of $l ₁^{m}$

Piotr Mankiewicz, Stanisław J. Szarek (2003)

Studia Mathematica

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We compare various constructions of random proportional quotients of $l ₁^{m}$ (i.e., with the dimension of the quotient roughly equal to a fixed proportion of m as m → ∞) and show that several of those constructions are equivalent. As a consequence of our approach we conclude that the most natural “geometric” models possess a number of asymptotically extremal properties, some of which were hitherto not known for any model.

Characterizing the powerset by a complete (Scott) sentence

Ioannis Souldatos (2013)

Fundamenta Mathematicae

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This paper is part II of a study on cardinals that are characterizable by a Scott sentence, continuing previous work of the author. A cardinal κ is characterized by a Scott sentence $ϕ_{ℳ}$ if $ϕ_{ℳ}$ has a model of size κ, but no model of size κ⁺. The main question in this paper is the following: Are the characterizable cardinals closed under the powerset operation? We prove that if $ℵ_{β}$ is characterized by a Scott sentence, then $2^{ℵ_{β + β ₁}}$ is (homogeneously) characterized by a Scott sentence, for all 0 <...

Ground states of supersymmetric matrix models

Gian Michele Graf (1998-1999)

Séminaire Équations aux dérivées partielles

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We consider supersymmetric matrix Hamiltonians. The existence of a zero-energy bound state, in particular for the $d = 9$ model, is of interest in M-theory. While we do not quite prove its existence, we show that the decay at infinity such a state would have is compatible with normalizability (and hence existence) in $d = 9$ . Moreover, it would be unique. Other values of $d$ , where the situation is somewhat different, shall also be addressed. The analysis is based on a Born-Oppenheimer approximation....

Positivity of quadratic base change $L$ -functions

Hervé Jacquet, Chen Nan (2001)

Bulletin de la Société Mathématique de France

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We show that certain quadratic base change $L$ -functions for $Gl (2)$ are non-negative at their center of symmetry.

Distortion and spreading models in modified mixed Tsirelson spaces

S. A. Argyros, I. Deliyanni, A. Manoussakis (2003)

Studia Mathematica

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The results of the first part concern the existence of higher order ℓ₁ spreading models in asymptotic ℓ₁ Banach spaces. We sketch the proof of the fact that the mixed Tsirelson space T[(ₙ,θₙ)ₙ], $θ_{n + m} \geq θ ₙ θ ₘ$ and $l i m_{n} θ ₙ^{1 / n} = 1$ , admits an $ℓ ₁^{ω}$ spreading model in every block subspace. We also prove that if X is a Banach space with a basis, with the property that there exists a sequence (θₙ)ₙ ⊂ (0,1) with $l i m_{n} θ ₙ^{1 / n} = 1$ , such that, for every n ∈ ℕ, $| | \sum_{k = 1}^{m} x_{k} | | \geq θ ₙ \sum_{k = 1}^{m} | | x_{k} | |$ for every ₙ-admissible block sequence ${(x_{k})}_{k = 1}^{m}$ of vectors in X, then there exists c...

Exponent of growth of polynomial mappings of $C^{2}$ into $C^{2}$

Jacek Chadzyński, Tadeusz Krasiński (1988)

Banach Center Publications

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Birational Finite Extensions of Mappings from a Smooth Variety

Marek Karaś (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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We present an example of finite mappings of algebraic varieties f:V → W, where V ⊂ kⁿ, $W \subset k^{n + 1}$ , and $F : k ⁿ \to k^{n + 1}$ such that ${F |}_{V} = f$ and gdeg F = 1 < gdeg f (gdeg h means the number of points in the generic fiber of h). Thus, in some sense, the result of this note improves our result in J. Pure Appl. Algebra 148 (2000) where it was shown that this phenomenon can occur when V ⊂ kⁿ, $W \subset k^{m}$ with m ≥ n+2. In the case V,W ⊂ kⁿ a similar example does not exist.