arXiv research

This paper proposes a new method to automatically learn optimal return functions in reinforcement learning.

A method to estimate functions of the return using its moments in reinforcement learning.

We show that the moments of the distribution of historic stock returns are in excellent agreement with the Heston model and not with the multiplicative model, which predicts power-law tails of volatility and stock returns. We also show that the mean realized variance of returns is a linear function of the number of day…

The paper analyzes elicitability of return risk measures and their scoring functions.

We consider returns of two Korean stock market indices, KOSPI and KOSDAQ index. Central parts of the probability distribution function of returns are well fitted by the Lorentzian distribution function. However, tail parts of the probability distribution function follow a power law behavior well. We found that the prob…

The study explains stock return distributions using reaction functions.

We present a simple microstructure model of financial returns that combines (i) the well-known ARFIMA process applied to tick-by-tick returns, (ii) the bid-ask bounce effect, (iii) the fat tail structure of the distribution of returns and (iv) the non-Poissonian statistics of inter-trade intervals. This model allows us…

The paper proposes a method to decompose value functions in RL for better understanding and prediction.

We present an algorithm for the decomposition of periodic financial return data into orthogonal factors of expected return and "systemic", "productive", and "nonproductive" risk. Generally, when the number of funds does not exceed the number of periods, the expected return of a portfolio is an affine function of its pr…

We study the dependence of volatility on the stock price in the stochastic volatility framework on the example of the Heston model. To be more specific, we consider the conditional expectation of variance (square of volatility) under fixed stock price return as a function of the return and time. The behavior of this fu…

Topological anomaly scores predict return curves in S&P 500 stocks

Theory integrates loss aversion into expected utility for monetary returns.

Motivated by the need for effectively summarising, modelling, and forecasting the distributional characteristics of intra-daily returns, as well as the recent work on forecasting histogram-valued time-series in the area of symbolic data analysis, we develop a time-series model for forecasting quantile-function-valued (…

In this paper we derive the exact solution of the multi-period portfolio choice problem for an exponential utility function under return predictability. It is assumed that the asset returns depend on predictable variables and that the joint random process of the asset returns and the predictable variables follow a vect…

Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an approximate scaling and heavy tails of the return distributions, long-ranged volat…

Learning an optimal policy from a multi-modal reward function is a challenging problem in reinforcement learning (RL). Hierarchical RL (HRL) tackles this problem by learning a hierarchical policy, where multiple option policies are in charge of different strategies corresponding to modes of a reward function and a gati…

Study sets a nontrivial upper limit on return forecasting accuracy.

We study the Heston model, where the stock price dynamics is governed by a geometrical (multiplicative) Brownian motion with stochastic variance. We solve the corresponding Fokker-Planck equation exactly and, after integrating out the variance, find an analytic formula for the time-dependent probability distribution of…

Forecast stock return distributions using neural networks.

In terms of the stock exchange returns, we compute the analytic expression of the probability distributions F{DAX,+} and F{DAX,-} of the normalized positive and negative DAX (Germany) index daily returns r(t). Furthermore, we define the alpha re-scaled DAX daily index positive returns r(t)^alpha and negative returns (-…

A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical and numerical results for this model in a special limiting case of a single-sca…

Study finds TVL doesn't predict cryptocurrency returns.

Starting from an exact relationship between news, threshold and price return distributions in the stationary state, I discuss the ability of the Ghoulmie-Cont-Nadal model of traders to produce fat-tailed price returns. Under normal conditions, this model is not able to transform Gaussian news into fat-tailed price retu…

This paper evaluates various loss functions for Transformer models in stock ranking.

We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic vari…

We investigate scaling and memory effects in return intervals between price volatilities above a certain threshold $q$ for the Japanese stock market using daily and intraday data sets. We find that the distribution of return intervals can be approximated by a scaling function that depends only on the ratio between the …

In their activity, the traders approximate the rate of return by integer multiples of a minimal one. Therefore, it can be regarded as a quantized variable. On the other hand, there is the impossibility of observing the rate of return and its instantaneous forward time derivative, even if we consider it as a continuous …

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

We show how to reduce the problem of computing VaR and CVaR with Student T return distributions to evaluation of analytical functions of the moments. This allows an analysis of the risk properties of systems to be carefully attributed between choices of risk function (e.g. VaR vs CVaR); choice of return distribution (p…

The paper explores how market-based returns depend on past trade values.

We develop an axiomatic theory of balance functions (future value functions) in the theory of interest that is derived from financial considerations and which applies to general regulated payment streams, including continuous payment streams. Balance functions exist and are unique up to an initial choice of deposit and…

An artificial agent for financial risk and returns' prediction is built with a modular cognitive system comprised of interconnected recurrent neural networks, such that the agent learns to predict the financial returns, and learns to predict the squared deviation around these predicted returns. These two expectations a…

For a functionally generated portfolio, there is a natural decomposition of the relative log-return into the log-change in the generating function and a drift process. In this note, this decomposition is extended to arbitrary stock portfolios by an application of Fisk-Stratonovich integration. With the extended methodo…

The $κ$-generalised distribution fits daily stock returns well.

We describe how the market-based average and volatility of the "actual" return, which the investors gain within their market sales, depend on the statistical moments, volatilities, and correlations of the current and past market trade values. We describe three successive approximations. First, we derive the dependence …

Study of historic stock returns distributions, highlighting asymmetry and outliers.

The statistical properties of the return intervals $τ_q$ between successive 1-min volatilities of 30 liquid Chinese stocks exceeding a certain threshold $q$ are carefully studied. The Kolmogorov-Smirnov (KS) test shows that 12 stocks exhibit scaling behaviors in the distributions of $τ_q$ for different thresholds $q$. …

The herd behavior of returns is investigated in Korean futures exchange market. It is obtained that the probability distribution of returns for three types of herding parameter scales as a power law $R^{-β}$ with the exponents $β=3.6$(KTB203) and 2.9(KTB209) in two kinds of Korean treasury bond. For our case since the…

This paper studies a continuous-time market where an agent, having specified an investment horizon and a targeted terminal mean return, seeks to minimize the variance of the return. The optimal portfolio of such a problem is called mean-variance efficient à la Markowitz. It is shown that, when the market coefficients a…

Modeling financial returns as conditionally independent random variables explains power-law tails.

Online learning rbfnet improves multi-horizon returns forecasts for financial time series.

This paper proposes an embedding-based neural network for more accurate investment return prediction.

Bid-ask spread is taken as an important measure of the financial market liquidity. In this article, we study the dynamics of the spread return and the spread volatility of four liquid stocks in the Chinese stock market, including the memory effect and the multifractal nature. By investigating the autocorrelation functi…

We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where the function oscillates more, while allocating the samples such that they are wel…

Model approximates market prices and returns without prior market dynamics.

Derives an approximate solution for power utility optimization under predictable returns.

An adaptive algorithm optimizes resource allocation with diminishing returns.

This paper describes a new method of bond portfolio optimization based on stochastic string models of correlation structure in bond returns. The paper shows how to approximate correlation function of bond returns, compute the optimal portfolio allocation using Wiener-Hopf factorization, and check whether a collection o…