arXiv research

Bounds on long-term returns of leveraged ETFs are given.

Estimates returns for dollar cost averaging using geometric Brownian motion.

Study sets a nontrivial upper limit on return forecasting accuracy.

The study bounds the utility of empirically optimal portfolios using stock return data.

The signal-noise ratio of a portfolio of p assets, its expected return divided by its risk, is couched as an estimation problem on the sphere. When the portfolio is built using noisy data, the expected value of the signal-noise ratio is bounded from above via a Cramer-Rao bound, for the case of Gaussian returns. The bo…

Geometrically convex return risk measures on AM-algebras

Batch Reinforcement Learning (RL) algorithms attempt to choose a policy from a designer-provided class of policies given a fixed set of training data. Choosing the policy which maximizes an estimate of return often leads to over-fitting when only limited data is available, due to the size of the policy class in relatio…

We consider the evolution of scale-free networks according to preferential attachment schemes and show the conditions for which the exponent characterizing the degree distribution is bounded by upper and lower values. Our framework is an agent model, presented in the context of economic networks of trades, which shows …

The paper limits the profitability of technical trading rules and finds they are not better than random trading.

The risk premium is one of main concepts in mathematical finance. It is a measure of the trade-offs investors make between return and risk and is defined by the excess return relative to the risk-free interest rate that is earned from an asset per one unit of risk. The purpose of this article is to determine upper and …

New self-imitation learning method improves performance in continuous control tasks.

We analyze cross-correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of 1000 US stocks for the 2-yr period 1994--95 (ii) 30-min returns of 881 US stock…

The deep Q-network (DQN) and return-based reinforcement learning are two promising algorithms proposed in recent years. DQN brings advances to complex sequential decision problems, while return-based algorithms have advantages in making use of sample trajectories. In this paper, we propose a general framework to combin…

A new statistical concept, lepto-variance, is defined for stock returns using Regression Trees.

We show that in a large class of stochastic volatility models with additional skew-functions (local-stochastic volatility models) the tails of the cumulative distribution of the log-returns behave as exp(-c|y|), where c is a positive constant depending on time and on model parameters. We obtain this estimate proving a …

Paper presents a deep learning method for estimating asset return precision matrices in noisy financial markets.

Paper develops a new estimator for MDPs' risk functionals with lower variance and bias.

Develops geometric BSDEs for modeling dynamic return risk measures.

We consider the tail probabilities of stock returns for a general class of stochastic volatility models. In these models, the stochastic differential equation for volatility is autonomous, time-homogeneous and dependent on only a finite number of dimensional parameters. Three bounds on the high-volatility limits of the…

Continuous Hidden Markov Models for Equity Returns

New algorithms for efficient return distribution approximation in reinforcement learning.

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…

We provide a written proof of a result due to H. Minakawa, which states that all suspension Anosov flows generated by hyperbolic matrices with positive trace are pairwise almost equivalent. The proof relies on constructing, for any given suspension flow, a genus-one Birkhoff section whose first-return map has fewer fix…

This paper improves reinforcement learning by estimating return distributions using quantiles.

This paper improves reinforcement learning by estimating return distributions using quantiles.

We consider a discrete-time, linear state equation with delay which arises as a model for a trader's account value when buying and selling a risky asset in a financial market. The state equation includes a nonnegative feedback gain $α$ and a sequence $v(k)$ which models asset returns which are within known bounds but o…

A new model optimizes portfolios by learning stock return distributions conditioned on factors.

Proposes new rule for ranking investment prospects over long horizons.

Simpler majority vote of three classifiers achieves optimal error bounds.

The paper analyzes bank decisions in a three-step model, focusing on equity and debt raising.

This paper aims at developing a new method by which to build a data-driven portfolio featuring a target risk-return. We first present a comparative study of recurrent neural network models (RNNs), including a simple RNN, long short-term memory (LSTM), and gated recurrent unit (GRU) for selecting the best predictor to u…

Ridge leverage scores provide a balance between low-rank approximation and regularization, and are ubiquitous in randomized linear algebra and machine learning. Deterministic algorithms are also of interest in the moderately big data regime, because deterministic algorithms provide interpretability to the practitioner …

Let Mod(S) denote the mapping class group of a compact, orientable surface S. We prove that finitely generated subgroups of Mod(S) which are not virtually abelian have uniform exponential growth with minimal growth rate bounded below by a constant depending only, and necessarily, on S. For the proof, we find in any suc…

Understanding generalization in reinforcement learning (RL) is a significant challenge, as many common assumptions of traditional supervised learning theory do not apply. We focus on the special class of reparameterizable RL problems, where the trajectory distribution can be decomposed using the reparametrization trick…

Study on distributional TD learning with linear approximations for better return estimation.

A refinement of Bennett's inequality is introduced which is strictly tighter than the classical bound. The new bound establishes the convergence of the average of independent random variables to its expected value. It also carefully exploits information about the potentially heterogeneous mean, variance, and ceiling of…

New method for distributional off-policy evaluation using Bellman residual minimization.

The paper sets limits on the accuracy of macroeconomic forecasts based on statistical moments and trade volumes.

Unified framework for optimizing portfolios with distributions over weights, returns, and parameters.

Investors can achieve optimal risk-reward trade-offs with bonds and stocks under mean-reverting stock returns.

We provide explicit conditions on the distribution of risk-neutral log-returns which yield sharp asymptotic estimates on the implied volatility smile. We allow for a variety of asymptotic regimes, including both small maturity (with arbitrary strike) and extreme strike (with arbitrary bounded maturity), extending previ…

SmartDCA improves investment returns by adjusting purchases based on prices.

Cryptocurrencies show stable prices as a medium of exchange.

In this paper, we study a certain class of online optimization problems, where the goal is to maximize a function that is not necessarily concave and satisfies the Diminishing Returns (DR) property under budget constraints. We analyze a primal-dual algorithm, called the Generalized Sequential algorithm, and we obtain t…

The CAPM's market returns are endogenously determined, affecting all assets' expected returns.

Using zippered rectangle coordinates we parametrize a Poincaré section for horocycle flow on the space of genus 2 translation surfaces with one singular cone point of angle $6π$. In addition, we bound the return time under horocycle flow to this Poincaré section by examining a subset of surfaces where a certain sum of …

We present a detailed analysis of \emph{observable} moments based parameter estimators for the Heston SDEs jointly driving the rate of returns $R_t$ and the squared volatilities $V_t$. Since volatilities are not directly observable, our parameter estimators are constructed from empirical moments of realized volatilitie…

A method to assess sensitivity to unmeasured confounding with sharp bounds.