arXiv research

Dual representations for robust risk measures and uncertainty sets.

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…

Develops a framework for robust RL with dynamic risk measures.

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…

Study systemic risk measures adjusted to financial markets.

The paper studies robust risk measures with linear penalties under uncertain distributions.

This paper improves the robustness of risk estimation for financial positions.

We study issues of robustness in the context of Quantitative Risk Management and Optimization. We develop a general methodology for determining whether a given risk measurement related optimization problem is robust, which we call "robustness against optimization". The new notion is studied for various classes of risk …

Bayesian approach to robust risk measures under model uncertainty.

Paper quantifies distortion risk measures' robustness to distributional uncertainty.

The paper develops robust risk measures for uncertain loss positions.

Unified framework for robust risk measures beyond convexity.

A new framework for robust risk measurement and portfolio optimization.

We characterize when a convex risk measure associated to a law-invariant acceptance set in $L^\infty$ can be extended to $L^p$, $1\leq p<\infty$, preserving finiteness and continuity. This problem is strongly connected to the statistical robustness of the corresponding risk measures. Special attention is paid to concre…

Framework for quantifying uncertainty in dynamic processes.

Develops a new method for robust risk measurement by averaging nearby payoffs.

The paper refines and generalizes worst-case law invariant convex risk measures.

Novel framework for risk-sensitive reinforcement learning with robustness against uncertainty.

Study optimal risk sharing in decentralized peer-to-peer markets with robust risk measures.

We propose a robust risk measurement approach that minimizes the expectation of overestimation plus underestimation costs. We consider uncertainty by taking the supremum over a collection of probability measures, relating our approach to dual sets in the representation of coherent risk measures. We provide results that…

Paper proposes robust risk measures for non-negative risks with partial information.

The paper introduces a new measure of robustness for partially identifiable risks.

We develop robust Markov Decision Processes with risk measures for uncertain environments.

The paper proposes a new approach to model risk measurement based on the Wasserstein distance between two probability measures. It formulates the theoretical motivation resulting from the interpretation of fictitious adversary of robust risk management. The proposed approach accounts for equivalent and non-equivalent p…

This paper gives an overview of the theory of dynamic convex risk measures for random variables in discrete time setting. We summarize robust representation results of conditional convex risk measures, and we characterize various time consistency properties of dynamic risk measures in terms of acceptance sets, penalty …

New approach for prudent risk evaluation using model aggregation.

Study optimizes natural resource harvesting under model uncertainty using risk measures.

Accounting for model uncertainty in risk management and option pricing leads to infinite dimensional optimization problems which are both analytically and numerically intractable. In this article we study when this hurdle can be overcome for the so-called optimized certainty equivalent risk measure (OCE) -- including t…

Paper characterizes star-shaped risk measures and their properties.

In this paper we look at the efficacy of different risk measures on energy markets and across several different stock market indices. We use both the Value at Risk and the Tail Conditional Expectation on each of these data sets. We also consider several different durations and levels for historical risk measures. Throu…

In this paper, we present a unified framework for decision making under uncertainty. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision given the exact distribution of uncertain model parameters, and the outer risk measure quantifies the risk tha…

Surveying risk measures for handling uncertainty in various fields.

In the present contribution we characterize law determined convex risk measures that have convex level sets at the level of distributions. By relaxing the assumptions in Weber (2006), we show that these risk measures can be identified with a class of generalized shortfall risk measures. As a direct consequence, we are …

Motivated by optimal investment problems in mathematical finance, we consider a variational problem of Neyman-Pearson type for law-invariant robust utility functionals and convex risk measures. Explicit solutions are found for quantile-based coherent risk measures and related utility functionals. Typically, these solut…

Risk-averse model uncertainty framework for safe reinforcement learning.

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…

Proposes a risk parity portfolio optimization method that accounts for uncertainty in asset returns.

Monitoring means to observe a system for any changes which may occur over time, using a monitor or measuring device of some sort. In this paper we formulate a problem of monitoring dates of maximal risk of a financial position. Thus, the systems we are going to observe arise from situations in finance. The measuring de…

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…

New vine copula method forecasts portfolio risk measures robust to market downturns.

Develops a statistical framework for coherent risk estimation.

Improves reinforcement learning policies for robustness.

This paper investigates calculations of robust funding valuation adjustment (FVA) for over the counter (OTC) derivatives under distributional uncertainty using Wasserstein distance as the ambiguity measure. Wrong way funding risk can be characterized via the robust FVA formulation. The simpler dual formulation of the r…

This paper examines how data affects risk measures in uncertain distributions.

This paper investigates calculations of robust XVA, in particular, credit valuation adjustment (CVA) and funding valuation adjustment (FVA) for over-the-counter derivatives under distributional uncertainty using Wasserstein distance as the ambiguity measure. Wrong way counterparty credit risk and funding risk can be ch…

Paper proposes a new model for multivariate risk measures using Wasserstein barycenters.

Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticised for issues relating to backtesting. In particular, ES has been found not to be elicitable which means that backtesting for ES is less straightforward…

This work evaluates risks over time using robust measures and neural networks.