arXiv research

New sampling and identity-testing methods for mixtures of distributions that don't satisfy approximate tensorization of entropy.

We provide a complete characterization of the class of one-dimensional time-homogeneous diffusions consistent with a given law at an exponentially distributed time using classical results in diffusion theory. To illustrate we characterize the class of diffusions with the same distribution as Brownian motion at an expon…

Study extreme-case Value-at-Risk under IFR distributions, providing guidance for risk management.

We study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. While at shorter microscopic time lags the distribution has power-law tails, for mesoscopic times the bulk of the distribution (more than 99% of the probability) follows an expon…

The paper derives risk measures for metalog distributions.

In this paper, we generalize the parametric delta-VaR method from portfolios with normally distributed risk factors to portfolios with elliptically distributed ones. We treat both the expected shortfall and the Value-at-Risk of such portfolios. Special attention is given to the particular case of a multivariate t-distr…

The paper analyzes the risk of investing in a basket of 27 cryptocurrencies using statistical distributions.

Paper quantifies distortion risk measures' robustness to distributional uncertainty.

Researchers calculated EVaR for various distributions using Lambert function.

Investigates a new measure PELVE_n for risk assessment.

EX-DRL improves extreme quantile prediction for financial risk management.

DRL agents perform poorly at high decision frequencies, but a new algorithm improves performance.

Study optimal portfolio selection with Recovery Average Value at Risk, showing better control over liabilities.

A neural network estimates sampling distributions for hard problems where classical methods fail.

Some general features of kinetic multi-agent models are reviewed, with particular attention to the relation between the agent saving propensities and the form of the equilibrium wealth distribution. The effect of a finite cutoff of the saving propensity distribution on the corresponding wealth distribution is studied. …

We study the distributions of event-time returns and clock-time returns at different microscopic timescales using ultra-high-frequency data extracted from the limit-order books of 23 stocks traded in the Chinese stock market in 2003. We find that the returns at the one-trade timescale obey the inverse cubic law. For la…

Unexpectedly, weighted Pareto variables are stochastically dominant.

This study compares Bitcoin and S&P 500 returns using a new GTS distribution method.

Paper improves regret bounds for distributed experts problem.

The world GDP distribution is described using thermodynamics principles.

We study the shapes of the implied volatility when the underlying distribution has an atom at zero and analyse the impact of a mass at zero on at-the-money implied volatility and the overall level of the smile. We further show that the behaviour at small strikes is uniquely determined by the mass of the atom up to high…

We introduce a new statistical test of the hypothesis that a balanced panel of firms have the same growth rate distribution or, more generally, that they share the same functional form of growth rate distribution. We applied the test to European Union and US publicly quoted manufacturing firms data, considering functio…

We investigate the herd behavior of returns for the yen-dollar exchange rate in the Japanese financial market. It is obtained that the probability distribution $P(R)$ of returns $R$ satisfies the power-law behavior $P(R) \simeq R^{-β}$ with the exponents $β=3.11$(the time interval $τ=$ one minute) and 3.36($τ=$ one da…

Adversarial training (AT) is among the most effective techniques to improve model robustness by augmenting training data with adversarial examples. However, most existing AT methods adopt a specific attack to craft adversarial examples, leading to the unreliable robustness against other unseen attacks. Besides, a singl…

A new model forecasts Value-at-Risk using NIG distribution and dynamic scores.

New method for summarizing ranking distributions using consensus ranking distributions.

PostNet predicts uncertainty without OOD data, improving OOD detection and calibration.

Using Monte Carlo simulation to calculate the Value at Risk (VaR) as a possible risk measure requires adequate techniques. One of these techniques is the application of a compound distribution for the aggregates in a portfolio. In this paper, we consider the aggregated loss of Gamma distributed severities and estimate …

We analyse derivative securities whose value is NOT a deterministic function of an underlying which means presence of a basis risk at any time. The key object of our analysis is conditional probability distribution at a given underlying value and moment of time. We consider time evolution of this probability distributi…

We derive new approximations for the Value at Risk and the Expected Shortfall at high levels of loss distributions with positive skewness and excess kurtosis, and we describe their precisions for notable ones such as for exponential, Pareto type I, lognormal and compound (Poisson) distributions. Our approximations are …

A new tree model, GRST, improves option pricing without log-normality assumptions.

The paper optimizes insurance dividend payments and reinsurance strategies under specific distribution constraints.

MF-GLaM models improve stochastic simulator emulation with multifidelity data.

CP improves robustness against distribution shift using physics-informed structural causal models.

We analyze the data on personal income distribution from the Australian Bureau of Statistics. We compare fits of the data to the exponential, log-normal, and gamma distributions. The exponential function gives a good (albeit not perfect) description of 98% of the population in the lower part of the distribution. The lo…

Improved variational inference for geophysical inverse problems with data correction.

This paper develops a communication-efficient algorithm to solve the stochastic optimization problem defined over a distributed network, aiming at reducing the burdensome communication in applications such as distributed machine learning.Different from the existing works based on quantization and sparsification, we int…

New $G_2$ symmetry found in 8D distribution with 6D square.

Deep neural networks forecast financial return distributions accurately.

Wasserstein gradient boosting predicts probability distributions for supervised learning.

The collection and analysis of user data drives improvements in the app and web ecosystems, but comes with risks to privacy. This paper examines discrete distribution estimation under local privacy, a setting wherein service providers can learn the distribution of a categorical statistic of interest without collecting …

We present ErasureHead, a new approach for distributed gradient descent (GD) that mitigates system delays by employing approximate gradient coding. Gradient coded distributed GD uses redundancy to exactly recover the gradient at each iteration from a subset of compute nodes. ErasureHead instead uses approximate gradien…

The paper analyzes extreme risk measures with limited distributional information.

Improved quantile estimation model for VaR.

New model optimizes oil product distribution via pipelines.

This dissertation reports work where physics methods are applied to financial and economical problems. The first part studies stock market data (chapter 1 to 5). The second part is devoted to personal income in the USA (chapter 6). We first study the probability distribution of stock returns at mesoscopic time lags (re…

The last decades have seen a surge of interests in distributed computing thanks to advances in clustered computing and big data technology. Existing distributed algorithms typically assume {\it all the data are already in one place}, and divide the data and conquer on multiple machines. However, it is increasingly ofte…

In this paper, we generalize the parametric Delta-VaR methods from portfolios with elliptic distributed risk factors to portfolios with mixture of elliptically distributed ones. We treat both the Expected Shortfall and the Value-at-Risk of such portfolios. Special attention is given to the particular case of the mixtur…