arXiv research

Two models incorporate market microstructure noise into asset pricing and option valuation.

Study shows mutual funds add little value for uninformed investors.

Following the statistical mechanics methodology, firstly introduced in macroeconomics by Aoki [1996,2002], we provide some insights to the well known works of Greenwald and Stiglitz [1990, 1993]. Specifically, we reach analytically a closed form solution of their models overcoming the aggregation problem. The key idea …

We define the LS-category cat_g by means of covers of a space by general subsets, and show that this definition coincides with the classical Lusternik-Schnirelmann category for compact metric ANR spaces. We apply this result to give short dimension theoretic proofs of the Grossman-Whitehead theorem and Dranishnikov's t…

We study a continuous-time version of the intermediation model of Grossman and Miller (1988). To wit, we solve for the competitive equilibrium prices at which liquidity takers' demands are absorbed by dealers with quadratic inventory costs, who can in turn gradually transfer these positions to an exogenous open market …

Post-groupoids help solve Yang-Baxter equation using quivers.

A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a drawdown constraint, as in the original setup of Grossman and Zhou (1993). We wor…

The Mutual Fund Theorem (MFT) is considered in a general semimartingale financial market S with a finite time horizon T, where agents maximize expected utility of terminal wealth. It is established that: 1) Let N be the wealth process of the numéraire portfolio (i.e. the optimal portfolio for the log utility). If any p…

We investigate the minimal and isoperimetric surface problems in a large class of sub-Riemannian manifolds, the so-called Vertically Rigid spaces. We construct an adapted connection for such spaces and, using the variational tools of Bryant, Griffiths and Grossman, derive succinct forms of the Euler-Lagrange equations …

We show that many normal subgroups of the braid group modulo its centre, and of the mapping class group of a sphere with marked points, have the property that their automorphism and abstract commensurator groups are mapping class groups of such spheres. As one application, we establish the automorphism groups of each t…

Elliptic curves and braid groups linked through configuration spaces.

We consider numerical integrators of ODEs on homogeneous spaces (spheres, affine spaces, hyperbolic spaces). Homogeneous spaces are equipped with a built-in symmetry. A numerical integrator respects this symmetry if it is equivariant. One obtains homogeneous space integrators by combining a Lie group integrator with an…

Let $\mathcal M (Σ, \mathcal P)$ be the mapping class group of a punctured oriented surface $(Σ, \mathcal P)$ (where $\mathcal P$ may be empty), and let $\mathcal T_p(Σ,\mathcal P)$ be the kernel of the action of $\mathcal M (Σ, \mathcal P)$ on $H_1 (Σ\setminus \mathcal P, \mathbb F_p)$. We prove that $\mathcal T_p(Σ, …

This work explores algebraic structures from curvature and torsion in affine connections.

Developing accurate, transferable and computationally inexpensive machine learning models can rapidly accelerate the discovery and development of new materials. Some of the major challenges involved in developing such models are, (i) limited availability of materials data as compared to other fields, (ii) lack of unive…

Optimal algorithm for selecting high-quality arms from infinite bandit arms.