Paper approximates Kelly betting for wealth growth.
problem Optimizing wealth growth in Kelly betting.
method Taylor-based approximation for quadratic programming.
result Closed-form approximate solution with interesting properties.
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48 results for “expected logarithmic growth”
Study growth of systoles in arithmetic manifolds, focusing on -dimensional cases.
problem Growth of systoles in arithmetic -manifolds along congruence coverings.
method Analyzes growth of -dimensional systoles in arithmetic -manifolds, proving polylogarithmic and constant power bounds.
result Growth of systoles for oscillates between a power of a logarithm and a power function of the degree of the covering.
Directly proves logarithmic systolic growth for all hyperbolic surfaces.
problem Proving logarithmic systolic growth for all hyperbolic surfaces.
method Using original Brooks/Buser-Sarnak surfaces through a direct approach.
result Directly proves logarithmic systolic growth for all hyperbolic surfaces.
This paper examines limitations of Kelly Criterion in gambling.
problem Limitations of the Kelly Criterion in gambling.
method Provided specific examples and described research directions.
result Quantified difficulties with Taylor-style approximations and wealth drawdowns.
Study shows logarithmic growth in systole for arithmetic spaces.
problem Understanding systole growth in arithmetic locally symmetric spaces.
method Examined congruence covers and showed logarithmic growth in systole.
result Logarithmic growth in systole is at least as large as volume.
We present a simple dynamical model of stock index returns which is grounded on the ability of the Cyclically Adjusted Price Earning (CAPE) valuation ratio devised by Robert Shiller to predict long-horizon performances of the market. More precisely, we discuss a discrete time dynamics in which the return growth depends…
Kelly investing improved with options to reduce estimation risk.
problem Estimation risk in Kelly investing leads to suboptimal portfolios.
method Introduced European options into the Kelly framework in a binomial model.
result Constructed growth optimal portfolios robust to estimation risk.
Study growth of LP wealth in G3Ms affected by trading fees and arbitrage.
problem Analyzing profitability of LPs in G3Ms under trading fees and arbitrage.
method Stochastic reflected diffusion processes to model G3M dynamics.
result Long-term expected logarithmic growth of LP wealth calculated.
Gambles are random variables that model possible changes in monetary wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes. Utility functions aim to capture individual psychological characteristics, but thei…
This paper explores using nonlinear control for robust logarithmic growth in coin flipping games.
problem Tackles the use of nonlinear control in recursive betting games with logarithmic growth.
method Formulates a robust nonlinear control problem for a simple coin flipping game, considering a probability range for the coin's bias.
result Provides a closed-form description of the optimal robust nonlinear controller, which outperforms linear controllers.
Numeraire marketsq-fin.MF
We study numeraire markets in open stock markets.
problem Understanding the numeraire portfolio in open stock markets.
method Constructed an example of a numeraire market that is asymptotically stable.
result Found an asymptotically stable numeraire market in open stock markets.
We consider the problem of optimizing the expected logarithmic utility of the value of a portfolio in a binomial model with proportional transaction costs with a long time horizon. By duality methods, we can find expressions for the boundaries of the no-trade-region and the asymptotic optimal growth rate, which can be …
The Impact of Execution Delay on Kelly-Based Stock Trading: High-Frequency Versus Buy and Holdmath.OC
Study compares high-frequency trading vs. buy and hold in stock markets with and without execution delay.
problem Impact of trade execution delay on Kelly-based stock trading strategies.
method Comparison of high-frequency trading and buy and hold strategies using Kelly's criterion and simulation.
result Buy and hold can outperform high-frequency trading with execution delay, contrary to intuition.
Mathematical study of excess growth rate connects info theory with finance.
problem Understanding the excess growth rate in portfolio theory.
method Axiomatic characterization theorems of excess growth rate in terms of relative entropy, Jensen's inequality gap, and logarithmic divergence.
result Established rich connections between information theory and finance.
Geodesics grow infinitely in certain Finsler manifolds.
problem Understanding the growth of geodesic chords in Finsler manifolds.
method Analyzing properties of forward complete Finsler manifolds with infinite fundamental group.
result Geodesics grow infinitely in specific Finsler manifolds.
A spring-block analogy for the dynamics of stock indexesphysics.soc-ph
A spring-block chain placed on a running conveyor belt is considered for modeling stylized facts observed in the dynamics of stock indexes. Individual stocks are modeled by the blocks, while the stock-stock correlations are introduced via simple elastic forces acting in the springs. The dragging effect of the moving be…
Consider the one-parameter generalizations of the logarithmic and exponential functions which are obtained from the integration of non-symmetrical hyperboles. These generalizations coincide to the one obtained in the context of non-extensive thermostatistics. We show that these functions are suitable to describe and un…
Random surfaces' diameter grows logarithmically with size.
problem Estimating the diameter of random hyperbolic surfaces.
method Uniform gluing of triangles, compactification, asymptotic analysis.
result The diameter is asymptotic to .
Paper proposes a method to solve log-optimal portfolios under ambiguous return distributions.
problem Maximizing wealth growth with unknown return distributions.
method Supporting hyperplane approximation to reformulate the problem into a linear program.
result The problem can be solved efficiently, even with transaction costs and diversification.
New control strategy mitigates stock trading drawdowns.
problem Mitigating drawdowns in stock trading.
method Drawdown-modulated feedback control using control theory.
result Optimal investment strategy that maximizes logarithmic growth.
Study shows Reeb orbits on starshaped hypersurfaces grow logarithmically with period.
problem Analyzing geometric properties of Reeb orbits on starshaped hypersurfaces.
method Proves logarithmic growth of Reeb orbits' number with period.
result Number of Reeb orbits grows at least logarithmically in period.
Optimizing betting frequency in dynamic games with Kelly criterion.
problem Finding the optimal betting frequency in a dynamic game setting.
method Using Kelly's expected logarithmic growth criterion, the study analyzes the performance of high-frequency and low-frequency bettors.
result The optimal performance gn* changes with n, and the high-frequency case does not always lead to the best performance.
In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that always implies logarithmic utility. The two approaches seem incompatible, too loos…
The Kelly Criterion is applied to prediction markets to analyze risk and return.
problem Mean beliefs in prediction markets often differ from actual prices.
method Logarithmic utility and Kullback-Leibler divergence are used to study risk and return adjustments.
result Misjudgment of bias and investment fraction affect portfolio growth rate.
Study preferences over uncertain time payments, finds growth-optimality better than expected utility theory.
problem Understanding how people make decisions with uncertain timing of payments.
method Normative model of growth-optimality, revisiting experimental evidence on time lotteries.
result Growth-optimality better explains experimental data on time lotteries than expected discounted utility theory.
Given for instance a finite volume negatively curved Riemannian manifold , we give a precise relation between the logarithmic growth rates of the excursions into cusps neighborhoods of the strong unstable leaves of negatively recurrent unit vectors of and their linear divergence rates under the geodesic flow. As…
We study the growth of the order of torsion subgroups of the homology in a tower of finite abelian coverings. In particular, we prove that it is exponential for when the tower converges to the maximal free abelian cover of a link complement when the first nonzero Alexander polynomial has positive logarithmic Mahler mea…
There are many industrial situations where rods are used to stir a fluid, or where rods repeatedly stretch a material such as bread dough or taffy. The goal in these applications is to stretch either material lines (in a fluid) or the material itself (for dough or taffy) as rapidly as possible. The growth rate of mater…
Develops a new option pricing model under G-expectation framework.
problem Modeling uncertainty in financial markets and robust valuation under model uncertainty.
method G-expectation framework, logarithmic transformation, finite difference schemes.
result Unified risk-neutral valuation approach yielding G-Black-Scholes equation.
This paper analyzes the robust growth rate of leveraged ETFs under uncertain parameters.
problem Analyzing the robust long-term growth rate of leveraged ETFs with uncertain parameters.
method Derive worst-case parameters using comparison principle and martingale extraction method.
result Explicitly obtain robust long-term growth rates under various models.
Generative AI predicts economic activity from corporate transcripts.
problem Predicting economic activity using existing measures like surveys.
method Extracted managerial expectations from transcripts using generative AI.
result AI Economy Score predicts economic activity up to 10 quarters ahead.
Study shows exponential growth of Laplacian determinant on random hyperbolic surfaces.
problem Understanding the behavior of Laplacian determinants on random hyperbolic surfaces.
method Investigated various models of random hyperbolic surfaces and their Laplacian determinants as genus increases.
result For all popular models, the determinant grows exponentially with a universal exponent as the genus goes to infinity.
New bounds reveal double exponential growth in conjugacy classes of fully irreducibles.
problem Counting conjugacy classes of fully irreducibles in Out(F_r).
method Equivalence to pseudo-Anosovs and logarithmic dilatations.
result Double exponential growth in the number of conjugacy classes.
Minimal hyperbolic surface diameter grows logarithmically with genus.
problem Finding the smallest possible diameter of hyperbolic surfaces.
method Random construction, lattice point counting, and exploration of random trivalent graphs.
result Minimal diameter is asymptotic to log(g) as genus g approaches infinity.
Fenchel-Willmore and Sobolev-type inequalities for submanifolds in non-negatively curved manifoldsmath.DG
Paper connects Fenchel-Willmore and Sobolev inequalities for submanifolds in curved spaces.
problem Developing inequalities for submanifolds in curved spaces.
method Connecting Fenchel-Willmore and logarithmic Sobolev inequalities for mean-convex submanifolds.
result Established extensions of Fenchel-Willmore inequality and derived new Sobolev-type inequalities.
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 …
Random surfaces with long systoles created from graph theory ideas.
problem Finding surfaces with long systoles.
method Two constructions inspired by graph theory.
result Proved a new lower bound on systole length.
A strategy ensures maximal wealth growth in competitive asset markets.
problem Maximizing wealth growth in competitive asset markets.
method Game-theoretic model and proof of existence of a submartingale strategy.
result Existence and uniqueness of a submartingale strategy that maximizes wealth growth.
Study 2-complexes' homology properties and torsion growth.
problem Quantitative connections between 1-cycle filling inequalities and homology complexities.
method Geometric lower bounds on first homology of finite covers.
result Geometric lower bound on first homology size of finite covers.
Investment and consumption strategy optimized under uncertain conditions.
problem Optimal investment and consumption under logarithmic utility and uncertainty model.
method Characterized using quadratic BSDE.
result Optimal solution found.
Logarithmic regret for continuous-time reinforcement learning.
problem Continuous-time Markov decision processes with unknown transition probabilities and holding times.
method Upper confidence reinforcement learning, mean holding time estimation, stochastic comparison of point processes.
result Logarithmic regret bound achieved in finite time.
Signature portfolios approximate optimal wealth in non-Markovian markets.
problem Approximating optimal wealth in non-Markovian markets.
method Linear path-functional portfolios based on signatures of market weights.
result Signature portfolios can uniformly approximate any continuous portfolio function.
Model shows consumption growth slows due to finite planet resources.
problem Understanding and predicting consumption growth in a finite planet context.
method Logistic model of consumption growth, cumulant expansion method.
result Social discount rates decline over time due to planetary resource constraints.
Study of holonomy behavior along differential rays on Riemann surfaces.
problem Analyzing the asymptotic behavior of holonomy along differential rays on Riemann surfaces.
method Investigates the asymptotic formulas for holonomy eigenvalues and growth rates using local fourth roots of the differential.
result Explicit asymptotic formulas for holonomy eigenvalues and their growth rates are derived.
In a financial market model, we consider variations of the problem of minimizing the expected time to upcross a certain wealth level. For exponential Levy markets, we show the asymptotic optimality of the growth-optimal portfolio for the above problem and obtain tight bounds for the value function for any wealth level.…
The paper addresses portfolio allocation with uncertain covariance matrices, finding a logarithmic risk dependence.
problem Portfolio allocation with uncertain covariance matrices.
method Calculates the expected value of CARA utility function over a distribution of covariance matrices, considering uncertainty in future returns and covariances.
result Marginalization introduces a logarithmic dependence on risk, leading to lower allocation levels for higher uncertainties.
We establish parabolicity and quadratic area growth for minimal surfaces-with-boundary contained in regions of R^3 which are within a sub-logarithmic factor of the exterior of a cone. Unlike previous work showing that these two properties hold for minimal surfaces-with-boundary contained between two catenoids, we do no…
Minimal geodesics on hyperbolic surfaces are long.
problem Finding the shortest closed geodesics on hyperbolic surfaces.
method Analyzing the self-intersection number to estimate geodesic lengths.
result The minimal length of geodesics grows logarithmically with the self-intersection number.