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.
When estimating the risk of a P&L from historical data or Monte Carlo simulation, the robustness of the estimate is important. We argue here that Hampel's classical notion of qualitative robustness is not suitable for risk measurement and we propose and analyze a refined notion of robustness that applies to tail-depend…
Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We characterize loss-based risk measures by a representation theorem and give examples of su…
Extended univariate Range Value-at-Risk to multivariate settings.
problem Inability of traditional risk measures for heavy-tail distributions and infinite tail expectations.
method Multivariate definitions of robust truncated tail expectations, robustness and properties derived, closed-form expressions and special cases discussed.
result Empirical estimators accuracy examined through numerical and graphical examples.
We provide a new computationally-efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models: in the classical Huber epsilon-contamination model and in heavy-tailed settings. Our workhorse is a novel robust variant of gradient descent, and we provide cond…
Recently, financial industry and regulators have enhanced the debate on the good properties of a risk measure. A fundamental issue is the evaluation of the quality of a risk estimation. On the one hand, a backtesting procedure is desirable for assessing the accuracy of such an estimation and this can be naturally achie…
Develops a statistical framework for coherent risk estimation.
problem Constructing coherent risk estimators with sound financial and statistical properties.
method Inspired by axiomatic risk measure theory, defines coherent risk estimators through robust representations linked to L-estimators.
result Demonstrates that coherence of a risk measure does not necessarily carry over to its estimators and shows alternative weight structures can lead to different outcomes.
Cross-validation under sample selection bias can, in principle, be done by importance-weighting the empirical risk. However, the importance-weighted risk estimator produces sub-optimal hyperparameter estimates in problem settings where large weights arise with high probability. We study its sampling variance as a funct…
Paper develops a robust hedging framework to reduce market risk and uncertainty.
problem Managing uncertainty and risk exposure in portfolio management.
method Combines high-frequency realized variance, covariance measures, and autoregressive models for multi-step volatility forecasting. Uses a box-uncertainty robust optimization scheme to derive a closed-form solution for the robust hedge ratio.
result Robust hedge ratios are more stable and entail lower turnover than standard dynamic hedges, improving downside protection and risk-adjusted performance.
Despite their numerous successes, there are many scenarios where adversarial risk metrics do not provide an appropriate measure of robustness. For example, test-time perturbations may occur in a probabilistic manner rather than being generated by an explicit adversary, while the poor train--test generalization of adver…
This paper investigates robust versions of the general empirical risk minimization algorithm, one of the core techniques underlying modern statistical methods. Success of the empirical risk minimization is based on the fact that for a "well-behaved" stochastic process {f(X),f∈F} indexed b…
Novel framework for risk-sensitive reinforcement learning with robustness against uncertainty.
problem Risk-sensitive reinforcement learning with uncertainty in transition dynamics.
method Developed a risk-sensitive robust Markov decision process (RSRMDP), derived its Bellman equation, and proposed a Bayesian Dynamic Programming (Bayesian DP) algorithm.
result Demonstrated convergence to near-optimal policies and analyzed sample and computational complexities.
Study enhances robustness of In-CVaR based regression models under perturbation and contamination.
problem Enhancing robustness of nonlinear regression models under perturbation and contamination.
method Introduces interval conditional value-at-risk (In-CVaR) and rigorously analyzes its robustness properties under both perturbation and contamination.
result The In-CVaR based estimator is qualitatively robust in terms of the Prokhorov metric if and only if the largest portion of losses is trimmed.
According to the Loss Distribution Approach, the operational risk of a bank is determined as 99.9% quantile of the respective loss distribution, covering unexpected severe events. The 99.9% quantile can be considered a tail event. As supported by the Pickands-Balkema-de Haan Theorem, tail events exceeding some high thr…
We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method minimizes a risk function defined by a non-parametric distribution with unknown prob…
From only positive (P) and unlabeled (U) data, a binary classifier could be trained with PU learning, in which the state of the art is unbiased PU learning. However, if its model is very flexible, empirical risks on training data will go negative, and we will suffer from serious overfitting. In this paper, we propose a…