arXiv research

Investigates the relationship between US money supply and asset indices over 2001-2019.

The paper simplifies string topology computations using Hochschild chain models.

It has been widely observed that capitalization-weighted indexes can be beaten by surprisingly simple, systematic investment strategies. Indeed, in the U.S. stock market, equal-weighted portfolios, random-weighted portfolios, and other naive, non- optimized portfolios tend to outperform a capitalization-weighted index …

In this paper we give the precise index growth for the embedded hypersurfaces of revolution with constant mean curvature (cmc) 1 in $\R^{n}$ (Delaunay unduloids). When $n=3$, using the asymptotics result of Korevaar, Kusner and Solomon, we derive an explicit asymptotic index growth rate for finite topology cmc 1 surfac…

Study growth rates of subgroups in groups with a constricting element.

We prove exponential growth rate of contractible closed geodesics for an arbitrary bumpy metric on manifolds of the form X#Y, where the fundamental group of X has a subgroup of finite index at least 3 and Y is simply connected and not a homotopy sphere.

We determine the factorial growth rate of the number of finite index subgroups of right-angled Artin groups as a function of the index. This turns out to depend solely on the independence number of the defining graph. We also make a conjecture for right-angled Coxeter groups and prove that it holds in a limited setting…

A portfolio of different stocks and a risk-less security whose composition is dynamically maintained stable by trading shares at any time step leads to a growth of the capital with a nonrandom rate. This is the key for the theory of optimal-growth investment formulated by Kelly. In presence of transaction costs, the op…

Let l be a link of d components. For every finite-index lattice in Z^d there is an associated finite abelian cover of S^3 branched over l. We show that the order of the torsion subgroup of the first homology of these covers has exponential growth rate equal to the logarithmic Mahler measure of the Alexander polynomial …

Optimizes portfolio growth rate for a behavioral investor considering terminal relative growth rate.

The paper models US inflation and hyperinflation using monetary and GDP data.

This note studies the behavior of an index I_t which is assumed to be a tradable security, to satisfy the BSM model dI_t/I_t = μdt + σdW_t, and to be efficient in the following sense: we do not expect a prespecified trading strategy whose value is almost surely always nonnegative to outperform the index greatly. The ef…

Optimal margin loan agreements for sophisticated gamblers and brokers.

In this article we consider a variant of Rabinowitz Floer homology in order to define a homological count of discriminant points for paths of contactomorphisms. The growth rate of this count can be seen as an analogue of Givental's nonlinear Maslov index. As an application we prove a Bott-Samelson type obstruction theo…

New algorithms optimize private convex optimization with faster rates for functions with κ-growth.

In this paper we investigate a new class of growth rate maximization problems based on impulse control strategies such that the average number of trades per time unit does not exceed a fixed level. Moreover, we include proportional transaction costs to make the portfolio problem more realistic. We provide a Verificatio…

Paper proves volume growth estimate for steady gradient Ricci solitons.

This paper analyzes the robust growth rate of leveraged ETFs under uncertain parameters.

We investigate the homology of finite index subgroups G_i of a given finitely presented group G. Specifically, we examine d_p(G_i), which is the dimension of the first homology of G_i, with mod p coefficients. We say that a collection of finite index subgroups {G_i} has linear growth of mod p homology if the infimum of…

Mathematical study of excess growth rate connects info theory with finance.

The paper derives index-energy estimates for Yang-Mills connections and Einstein metrics.

Zipf's law states that the number of firms with size greater than S is inversely proportional to S. Most explanations start with Gibrat's rule of proportional growth but require additional constraints. We show that Gibrat's rule, at all firm levels, yields Zipf's law under a balance condition between the effective grow…

Investigates optimal portfolio strategies in markets with latent side information.

We consider the problem of robustly maximizing the growth rate of investor wealth in the presence of model uncertainty. Possible models are all those under which the assets' region $E$ and instantaneous covariation $c$ are known, and where additionally the assets are stable in that their occupancy time measures converg…

Optimizes active and passive portfolio management using latent factors.

Study finds minimal hypersurfaces grow linearly in index, contrary to 3D.

Study shows torsion grows subexponentially in book of I-bundles but can grow exponentially in non-regular covers.

Study examines how COVID-19 affected India's exchange rates and stock market.

We consider the maximization of the long-term growth rate in the Black-Scholes model under proportional transaction costs as in Taksar, Klass and Assaf [Math. Oper. Res. 13, 1988]. Similarly as in Kallsen and Muhle-Karbe [Ann. Appl. Probab., 20, 2010] for optimal consumption over an infinite horizon, we tackle this pro…

Employing profits data of Japanese firms in 2003--2005, we kinematically exhibit the static log-normal distribution in the middle scale region. In the derivation, a Non-Gibrat's law under the detailed balance is adopted together with following two approximations. Firstly, the probability density function of profits gro…

Paper examines global Covid-19 data complexity and finds low intrinsic dimensions.

In this paper, a new theory is developed for first-order stochastic convex optimization, showing that the global convergence rate is sufficiently quantified by a local growth rate of the objective function in a neighborhood of the optimal solutions. In particular, if the objective function $F(\mathbf w)$ in the $ε$-sub…

Abstract Coxeter groups have growth rates that are Perron numbers.

In order to investigate whether government regulations against corruption can affect the economic growth of a country, we analyze the dependence between Gross Domestic Product (GDP) per capita growth rates and changes in the Corruption Perceptions Index (CPI). For the period 1999-2004 on average for all countries in th…

The paper finds the optimal wealth growth rate in betting games.

Study preferences over uncertain time payments, finds growth-optimality better than expected utility theory.

For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $λ\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading s…

A strategy ensures maximal wealth growth in competitive asset markets.

In 1979 following a decade of hyperinflation, Iceland introduced Verðtryggð lán, negatively amortised, index-linked loans whose outstanding principal is increased by the rate of the consumer price inflation index(CPI). The loans were part of a general government policy which used indexation to the CPI to address the ec…

Novel pricing method for equity-indexed annuities under uncertain volatility and stochastic interest rate.

We investigate the ergodic problem of growth-rate maximization under a class of risk constraints in the context of incomplete, Itô-process models of financial markets with random ergodic coefficients. Including {\em value-at-risk} (VaR), {\em tail-value-at-risk} (TVaR), and {\em limited expected loss} (LEL), these cons…

Exponential growth of stable subgroups in Morse geodesics.

Study shows convergence rate for empirical minimizer of unbounded functions with fast growth.

Paper introduces new risk measures for Kelly criterion.

The study shows how nonnegative Ricci curvature and metric cones imply the existence of abelian subgroups in the fundamental group of open manifolds.

Growth rates of geodesics on modular orbifolds are studied.

In finance, one usually deals not with prices but with growth rates $R$, defined as the difference in logarithm between two consecutive prices. Here we consider not the trading volume, but rather the volume growth rate $\tilde R$, the difference in logarithm between two consecutive values of trading volume. To this end…

This survey reviews portfolio selection problem for long-term horizon. We consider two objectives: (i) maximize the probability for outperforming a target growth rate of wealth process (ii) minimize the probability of falling below a target growth rate. We study the asymptotic behavior of these criteria formulated as l…