arXiv research

Defines new extremal potentials and measures for Kähler forms.

The paper calculates extreme measures in continuous time conic finance.

This paper applies the Extreme-Value (EV) Generalised Pareto distribution to the extreme tails of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses tail estimators from these contracts to estimate spectral risk measures, which are coherent risk measures that r…

Optimal portfolios for fat-tailed risks using a new tail risk measure.

Paper develops a novel approach to identify clusters of features in multivariate extremes.

Spectral clustering identifies clusters of multivariate extremes.

Risk is an inherent feature of agricultural production and marketing and accurate measurement of it helps inform more efficient use of resources. This paper examines three tail quantile-based risk measures applied to the estimation of extreme agricultural financial risk for corn and soybean production in the US: Value …

Paper improves risk estimation for extreme events.

The study introduces new liquidity measures and models for assets with extreme liquidity.

The paper analyzes extreme risk measures with limited distributional information.

Develops a new model for measuring extremal dependence in financial markets.

A meticulous assessment of the risk of impacts associated with extreme wind events is of great necessity for populations, civil authorities as well as the insurance industry. Using the concept of spatial risk measure and related set of axioms introduced by Koch (2017, 2019), we quantify the risk of losses due to extrem…

ExGAN generates realistic extreme samples using GANs and EVT.

The thesis evaluates and compares extreme mixture models in finance and insurance.

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

The paper provides bounds for the empirical angular measure and applies them to improve statistical learning in extreme regions.

Paper examines risk measure expansions under FGM dependence, improving accuracy at extreme levels.

Capturing the dependence structure of multivariate extreme events is a major concern in many fields involving the management of risks stemming from multiple sources, e.g. portfolio monitoring, insurance, environmental risk management and anomaly detection. One convenient (non-parametric) characterization of extremal de…

The paper calculates VaR and CTE for extreme and aggregate risks using FGM copula.

We investigate the supports of extremal martingale measures with pre-specified marginals in a two-period setting. First, we establish in full generality the equivalence between the extremality of a given measure $Q$ and the denseness in $L^1(Q)$ of a suitable linear subspace, which can be seen in a financial context as…

We study extreme values of group-indexed stable random fields for discrete groups $G$ acting geometrically on spaces $X$ in the following cases: 1) $G$ acts freely, properly discontinuously by isometries on a CAT(-1) space $X$, 2) $G$ is a lattice in a higher rank Lie group, acting on a symmetric space $X$, 3) $G$ is t…

The study measures systemic risk using common and tail dependence factors.

Extremal length is an important conformal invariant on Riemann surface. It is closely related to the geometry of Teichmuller metric on Teichmuller space. By identifying extremal length functions with energy of harmonic maps from Riemann surfaces to $\mathbb{R}$-trees, we study the second variation of extremal length fu…

This paper uses VAE to generate extreme events from multivariate data.

Non-convex extremal length found in surface metrics.

Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure - the spectral measure - defined on the positive orthant of the unit sphere. This measure gathers information on the localizat…

We define regular points of an extremal subset in an Alexandrov space and study their basic properties. We show that a neighborhood of a regular point in an extremal subset is almost isometric to an open subset in Euclidean space and that the set of regular points in an extremal subset has full measure and is dense in …

Paper derives best- and worst-case GlueVaR measures with incomplete data.

New method estimates root-directed tree from extreme data.

We consider strictly stationary heavy tailed time series whose finite-dimensional exponent measures are concentrated on axes, and hence their extremal properties cannot be tackled using classical multivariate regular variation that is suitable for time series with extremal dependence. We recover relevant information ab…

We consider learning the principal subspace of a large set of vectors from an extremely small number of compressive measurements of each vector. Our theoretical results show that even a constant number of measurements per column suffices to approximate the principal subspace to arbitrary precision, provided that the nu…

New method identifies key channels for extreme brain events.

Critical graphs of quadratic differentials equidistribute in moduli space.

This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a numéraire. It is shown that the presence of arbitrarily small stochastic deviations in the evolution of the numéraire process causes significant chang…

Study efficient resource allocation for detecting extreme values.

Kernel PCA helps analyze multivariate extremes and clusters them effectively.

Accurate forecasting of risk is the key to successful risk management techniques. Using the largest stock index futures from twelve European bourses, this paper presents VaR measures based on their unconditional and conditional distributions for single and multi-period settings. These measures underpinned by extreme va…

Closed-form pricing method for multi-asset options.

Estimates treatment effects in rare extreme events using EVT.

This paper develops a theory of Lipschitz comparisons of hyperbolic surfaces analogous to the theory of quasi-conformal comparisons. Extremal Lipschitz maps (minimal stretch maps) and geodesics for the `Lipschitz metric' are constructed. The extremal Lipschitz constant equals the maximum ratio of lengths of measured la…

Flexible XVAE model for efficient spatial extremes simulation.

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…

Proposes a network-based strategy to manage financial market risks.

Inference over tails is usually performed by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. However, the choice of such threshold is critical and can affect the inferential results. Extreme value mixture models have been defined to estimate the threshold using the full dat…

Study examines dependence of extreme electricity prices in Australian markets.

The price of electricity is far more volatile than that of other commodities normally noted for extreme volatility. The possibility of extreme price movements increases the risk of trading in electricity markets. However, underlying the process of price returns is a strong mean-reverting mechanism. We study this featur…

New method forecasts systemic risk with improved precision.

The paper has 2 main goals: 1. We propose a variant of the CAPM based on coherent risk. 2. In addition to the real-world measure and the risk-neutral measure, we propose the third one: the extreme measure. The introduction of this measure provides a powerful tool for investigating the relation between the first two mea…