A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A new tail-shape index based on Value at Risk and Expected Shortfall.
Heavy-tailed distributions emerge in SGD's parameter evolution.
The study introduces a high-dimensional tail index model for viral post analysis.
Kurtosis is seen as a measure of the discrepancy between the observed data and a Gaussian distribution and is defined when the 4th moment is finite. In this work an empirical study is conducted to investigate the behaviour of the sample estimate of kurtosis with respect to sample size and the tail index when applied to…
Cyclic and randomized stepsizes can lead to heavier tails in SGD, improving generalization.
Paper introduces a new robust method for estimating Pareto tail index from grouped data.
Paper proposes a risk index combining frequency and severity of abnormal driving patterns.
This paper analyzes bias-variance trade-off for clipped SFOMs, improving complexity guarantees for heavy-tailed noise.
We investigate the probability distribution of order imbalance calculated from the order flow data of 43 Chinese stocks traded on the Shenzhen Stock Exchange. Two definitions of order imbalance are considered based on the order number and the order size. We find that the order imbalance distributions of individual stoc…
Study reveals heavy-tailed behavior in training ReLU gates.
We study the problems related to the estimation of the Gini index in presence of a fat-tailed data generating process, i.e. one in the stable distribution class with finite mean but infinite variance (i.e. with tail index ). We show that, in such a case, the Gini coefficient cannot be reliably estimated usin…
Develops a robust model for skewed and heavy-tailed data in periodontal studies.
Study improves policy search in continuous control by using heavy-tailed distributions.
The book chapter discusses tail risk analysis for financial data using extreme value statistics.
Failure of the main argument for the use of heavy tailed distribution in Finance is given. More precisely, one cannot observe so many outliers for Cauchy or for symmetric stable distributions as we have in reality. keywords:outliers; financial indexes; heavy tails; Cauchy distribution; stable distributions
The study examines when large trades are considered news or liquidity shocks in a market model.
This paper analyzes ETFs with Taiwan exposure, finding heavy tails and asymmetric volatility.
Using daily returns of the S&P 500 stocks from 2001 to 2011, we perform a backtesting study of the portfolio optimization strategy based on the extreme risk index (ERI). This method uses multivariate extreme value theory to minimize the probability of large portfolio losses. With more than 400 stocks to choose from, ou…
Optimal algorithm for minimizing regret in heavy-tailed bandits.
We build a methodology that takes a given option price in the tails with strike and extends (for calls, all strikes > , for puts all strikes ) assuming the continuation falls into what we define as "Karamata Constant" over which the strong Pareto law holds. The heuristic produces relative prices for options…
AdaGrad converges under heavy-tailed noise without extra operations.
Bitcoin returns exhibit a distinct inverse cubic law scaling behavior.
Value at risk (VaR) is a risk measure that has been widely implemented by financial institutions. This paper measures the correlation among asset price changes implied from VaR calculation. Empirical results using US and UK equity indexes show that implied correlation is not constant but tends to be higher for events i…
We consider the problem of risk diversification of -stable heavy tailed risks. We study the behaviour of the aggregated Value-at-Risk, with particular reference to the impact of different tail dependence structures on the limits to diversification. We confirm the large evidence of sub-additivity violations, particul…
Based on a recent theorem due to the authors, it is shown how the extreme tail dependence between an asset and a factor or index or between two assets can be easily calibrated. Portfolios constructed with stocks with minimal tail dependence with the market exhibit a remarkable degree of decorrelation with the market at…
Paper proposes GAS-ALD model for financial risk prediction.
We propose a random walk model of asset returns where the parameters depend on market stress. Stress is measured by, e.g., the value of an implied volatility index. We show that model parameters including standard deviations and correlations can be estimated robustly and that all distributions are approximately normal.…
For a risk vector , whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by Value-at-Risk or Conditional Tail Expectation. We assume Pareto tails for the componen…
Recently, Mike and Farmer have constructed a very powerful and realistic behavioral model to mimick the dynamic process of stock price formation based on the empirical regularities of order placement and cancelation in a purely order-driven market, which can successfully reproduce the whole distribution of returns, not…
This paper presents a statistical analysis of Tehran Price Index (TePIx) for the period of 1992 to 2004. The results present asymmetric property of the return distribution which tends to the right hand of the mean. Also the return distribution can be fitted by a stable Levy distribution and the tails are very fatter th…
The paper uses EVT to improve tail risk measures under ambiguity sets.
Model monthly VIX and stock returns using log-Heston model.
The study measures systemic risk using common and tail dependence factors.
New model captures time-varying volatility with stochastic exponential tails.
A time series that represents daily values of the WIG index (the main index of Warsaw Stock Exchange) over last 5 years is examined. Non-Gaussian features of distributions of fluctuations, namely returns, over a time scale are considered. Some general properties like exponents of the long range correlation estimated by…
Distributions derived from non-extensive Tsallis statistics are closely connected with dynamics described by a nonlinear Fokker-Planck equation. The combination shows promise in describing stochastic processes with power-law distributions and superdiffusive dynamics. We investigate intra-day price changes in the S&P500…
We report empirical studies on the personal income distribution, and clarify that the distribution pattern of the lognormal with power law tail is the universal structure. We analyze the temporal change of Pareto index and Gibrat index to investigate the change of the inequality of the income distribution. In addition …
This work extends diffusion models to handle heavy-tailed targets, improving score estimation and sampling guarantees.
In the spirit of the emergent field of econophysics, a goodness-of-fit test for the Power-Law distribution, based on the Empirical Distribution Function (EDF) is presented, and related problems are discussed. An analysis of the tail behaviour of the daily logarithmic variation of the Mexican Stock Market Index (IPC), s…
Commodity ETFs' portfolio optimization under heavy-tailed returns.
The paper provides a new uniform tail bound for empirical processes.
We demonstrate that the tail dependence should always be taken into account as a proxy for systematic risk of loss for investments. We provide the clear statistical evidence of that the structure of investment portfolios on a regulated market should be adjusted to the price of gold. Our finding suggests that the active…
New framework controls generalization for heavy-tailed data in RLHF and SGLD.
The study examines tail dependence between global economic uncertainty and BRICS currencies using high-frequency data.
The gradient noise (GN) in the stochastic gradient descent (SGD) algorithm is often considered to be Gaussian in the large data regime by assuming that the \emph{classical} central limit theorem (CLT) kicks in. This assumption is often made for mathematical convenience, since it enables SGD to be analyzed as a stochast…
In this paper, we establish the stochastic ordering of the Gini indexes for multivariate elliptical risks which generalized the corresponding results for multivariate normal risks. It is shown that several conditions on dispersion matrices and the components of dispersion matrices of multivariate normal risks for the m…
Proposes a tail-adaptive shrinkage method for robust sparse estimation.
The SV-GARCH-EVT model improves risk assessment in financial markets.