arXiv research

The paper identifies and critiques problems with risk matrices using ordinal scales.

In this paper, we obtain a property of the expectation of the inverse of compound Wishart matrices which results from their orthogonal invariance. Using this property as well as results from random matrix theory (RMT), we derive the asymptotic effect of the noise induced by estimating the covariance matrix on computing…

Mirror descent algorithm recovers low-rank matrices in matrix sensing.

The paper addresses portfolio allocation with uncertain covariance matrices, finding a logarithmic risk dependence.

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…

We give an explicit algorithm and source code for constructing risk models based on machine learning techniques. The resultant covariance matrices are not factor models. Based on empirical backtests, we compare the performance of these machine learning risk models to other constructions, including statistical risk mode…

New method uses VAEs to generate financial correlation matrices for credit portfolio VaR analysis.

We analyze the condition number of random feature matrices and prove their well-conditioned nature.

We consider random-design linear prediction and related questions on the lower tail of random matrices. It is known that, under boundedness constraints, the minimax risk is of order $d/n$ in dimension $d$ with $n$ samples. Here, we study the minimax expected excess risk over the full linear class, depending on the dist…

cCorrGAN approximates conditional correlation matrices using GANs.

This note improves correlation stress tests using geodesic distance.

Financial correlation matrices measure the unsystematic correlations between stocks. Such information is important for risk management. The correlation matrices are known to be ``noise dressed''. We develop a new and alternative method to estimate this noise. To this end, we simulate certain time series and random matr…

Risk management is an important practice in the banking industry. In this paper we develop a new methodology to estimate and predict the probability of default (PD) based on the rating transition matrices, which relates the rating transition matrices to the macroeconomic variables. Our method can overcome the shortcomi…

This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been motivated by a large and growing use of matrix-valued affine processes in finance, including multi-asset option pricing with stochastic volatil…

We review recent progress in modeling credit risk for correlated assets. We start from the Merton model which default events and losses are derived from the asset values at maturity. To estimate the time development of the asset values, the stock prices are used whose correlations have a strong impact on the loss distr…

Dynamic risk assessment method for WUI fires improves upon static frameworks.

We introduce a simple approach for testing the reliability of homogeneous generators and the Markov property of the stochastic processes underlying empirical time series of credit ratings. We analyze open access data provided by Moody's and show that the validity of these assumptions - existence of a homogeneous genera…

Recent studies inspired by results from random matrix theory [1,2,3] found that covariance matrices determined from empirical financial time series appear to contain such a high amount of noise that their structure can essentially be regarded as random. This seems, however, to be in contradiction with the fundamental r…

A new method prioritizes project risks using Monte Carlo Simulation.

In this paper we propose a cyclical coordinate descent (CCD) algorithm for solving high dimensional risk parity problems. We show that this algorithm converges and is very fast even with large covariance matrices (n > 500). Comparison with existing algorithms also shows that it is one of the most efficient algorithms.

We propose a novel approach for sampling realistic financial correlation matrices. This approach is based on generative adversarial networks. Experiments demonstrate that generative adversarial networks are able to recover most of the known stylized facts about empirical correlation matrices estimated on asset returns.…

The article detects market regimes from covariance matrices using VLSTAR and clustering models.

Estimates KRR risk from training data for various kernels and hyperparameters.

Improved market state classification for risk assessment.

The following working document summarizes our work on the clustering of financial time series. It was written for a workshop on information geometry and its application for image and signal processing. This workshop brought several experts in pure and applied mathematics together with applied researchers from medical i…

New framework for calculating multivariate risk measures using Wishart process.

We investigate the high-dimensional regression problem using adjacency matrices of unbalanced expander graphs. In this frame, we prove that the $\ell_{2}$-prediction error and the $\ell_{1}$-risk of the lasso and the Dantzig selector are optimal up to an explicit multiplicative constant. Thus we can estimate a high-dim…

Enhanced Transformer models predict ETF portfolio performance by optimizing covariance and semi-covariance matrices.

This paper establishes risk convergence and asymptotic weight matrix alignment --- a form of implicit regularization --- of gradient flow and gradient descent when applied to deep linear networks on linearly separable data. In more detail, for gradient flow applied to strictly decreasing loss functions (with similar re…

Neural networks have been shown to be vulnerable against minor adversarial perturbations of their inputs, especially for high dimensional data under $\ell_\infty$ attacks. To combat this problem, techniques like adversarial training have been employed to obtain models which are robust on the training set. However, the …

Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for other methods the spectral information can be used to estimate the excess risk. An …

We study risk of the minimum norm linear least squares estimator in when the number of parameters $d$ depends on $n$, and $\frac{d}{n} \rightarrow \infty$. We assume that data has an underlying low rank structure by restricting ourselves to spike covariance matrices, where a fixed finite number of eigenvalues grow with…

Trace norm regularization is a popular method of multitask learning. We give excess risk bounds with explicit dependence on the number of tasks, the number of examples per task and properties of the data distribution. The bounds are independent of the dimension of the input space, which may be infinite as in the case o…

We propose a framework for constructing factor models for alpha streams. Our motivation is threefold. 1) When the number of alphas is large, the sample covariance matrix is singular. 2) Its out-of-sample stability is challenging. 3) Optimization of investment allocation into alpha streams can be tractable for a factor …

We analyze kernel matrices in polynomial high-dimensional settings and explain double descent in KRR.

We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations severely limits the effect of diversification in a credit portfolio if the corre…

Sharp risk bounds for early-stopping in Gaussian linear regression are derived.

Paper defines conditions for feasible correlation matrices from factor structures.

A new method for efficiently updating large-scale matrices in real-time.

Let $A:[0,1]\rightarrow\mathbb{H}_m$ (the space of Hermitian matrices) be a matrix valued function which is low rank with entries in Hölder class $Σ(β,L)$. The goal of this paper is to study statistical estimation of $A$ based on the regression model $\mathbb{E}(Y_j|τ_j,X_j) = \langle A(τ_j), X_j \rangle,$ where $τ_j$ …

Financial correlations play a central role in financial theory and also in many practical applications. From theoretical point of view, the key interest is in a proper description of the structure and dynamics of correlations. From practical point of view, the emphasis is on the ability of the developed models to provi…

According to recent findings [1,2], empirical covariance matrices deduced from financial return series contain such a high amount of noise that, apart from a few large eigenvalues and the corresponding eigenvectors, their structure can essentially be regarded as random. In [1], e.g., it is reported that about 94% of th…

In this work, we propose a PAC-Bayes bound for the generalization risk of the Gibbs classifier in the multi-class classification framework. The novelty of our work is the critical use of the confusion matrix of a classifier as an error measure; this puts our contribution in the line of work aiming at dealing with perfo…

The paper analyzes bagging in overparameterized learning, deriving risk properties and optimal subsample sizes.

Method cleans covariance matrices for better statistical inference.

When presented with Out-of-Distribution (OOD) examples, deep neural networks yield confident, incorrect predictions. Detecting OOD examples is challenging, and the potential risks are high. In this paper, we propose to detect OOD examples by identifying inconsistencies between activity patterns and class predicted. We …

High-dimensional random geometry shows phase transitions in various problems.

This paper develops a new portfolio optimization framework that considers network spillovers.