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This paper proposes a portfolio construction framework designed to remain robust under estimation error, non-stationarity, and realistic trading constraints. The methodology combines dynamic asset eligibility, deterministic rebalancing, and…
A (closed) dynamical system is a notion of how things can be, together with a notion of how they may change given how they are. The idea and mathematics of closed dynamical systems has proven incredibly useful in those sciences that can…
Portfolio optimisation is essential in quantitative investing, but its implementation faces several practical difficulties. One particular challenge is converting optimal portfolio weights into real-life trades in the presence of realistic…
We introduce a novel approach to portfolio optimization that leverages hierarchical graph structures and the Schur complement method to systematically reduce computational complexity while preserving full covariance information. Inspired by…
We develop a compositional framework for formal synthesis of hybrid systems using the language of category theory. More specifically, we provide mutually compatible tools for hierarchical, sequential, and independent parallel composition.…
We give a systematic approach to constructing non-reduced, locally Cohen-Macaulay schemes with reduced support a smooth projective variety. The hierarchy of such structures includes a lot of information about the underlying variety, its…
We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate…
We construct a deep portfolio theory. By building on Markowitz's classic risk-return trade-off, we develop a self-contained four-step routine of encode, calibrate, validate and verify to formulate an automated and general portfolio…
This document is centered around a main idea: simplicial categories, by which we mean simplicial objects in the category of categories, can be treated as a two-fold categorical structure and their double category theory is homotopically…
Applied category theory often studies symmetric monoidal categories (SMCs) whose morphisms represent open systems. These structures naturally accommodate complex wiring patterns, leveraging (co)monoidal structures for splitting and merging…
Portfolio optimization is a ubiquitous problem in financial mathematics that relies on accurate estimates of covariance matrices for asset returns. However, estimates of pairwise covariance could be better and calculating time-sensitive…
We extend logical categories with fiberwise interior and closure operators so as to obtain an embedding theorem into powers of the category of topological spaces. The required axioms, besides the Kuratowski closure axioms, are a `product…
We propose a unified approach to several problems in Stochastic Portfolio Theory (SPT), which is a framework for equity markets with a large number $d$ of stocks. Our approach combines open markets, where trading is confined to the top $N$…
Since the time when the first optical instruments have been invented, an idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way to formalize it in mathematics is…
Two-stage robust optimization is a fundamental paradigm for modeling and solving optimization problems with uncertain parameters. A now classical method within this paradigm is finite adaptability, introduced by Bertsimas and Caramanis…
Investment returns naturally reside on irregular domains, however, standard multivariate portfolio optimization methods are agnostic to data structure. To this end, we investigate ways for domain knowledge to be conveniently incorporated…
Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…
We define a class of non-compact Fano toric manifolds, called admissible toric manifolds, for which Floer theory and quantum cohomology are defined. The class includes Fano toric negative line bundles, and it allows blow-ups along fixed…
In a Systems Engineering setting, various models are produced using a variety of methods and tools. Focusing on a type of models -- called descriptive models -- which we shall describe, we argue that, while the clarity and precision of…
The idiosyncratic (microscopic) and systemic (macroscopic) components of market structure have been shown to be responsible for the departure of the optimal mean-variance allocation from the heuristic `equally-weighted' portfolio. In this…