Related papers: Submodular risk measures
The use of non-translation invariant risk measures within the equal risk pricing (ERP) methodology for the valuation of financial derivatives is investigated. The ability to move beyond the class of convex risk measures considered in…
We propose a new approach, termed Realized Risk Measures (RRM), to estimate Value-at-Risk (VaR) and Expected Shortfall (ES) using high-frequency financial data. It extends the Realized Quantile (RQ) approach proposed by Dimitriadis and…
Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is…
The estimation of risk measures recently gained a lot of attention, partly because of the backtesting issues of expected shortfall related to elicitability. In this work we shed a new and fundamental light on optimal estimation procedures…
We study dynamic risk measures in a very general framework enabling to model uncertainty and processes with jumps. We previously showed the existence of a canonical equivalence class of probability measures hidden behind a given set of…
Value at risk (VaR) and expected shortfall (ES) are common high quantile-based risk measures adopted in financial regulations and risk management. In this paper, we propose a tail risk measure based on the most probable maximum size of risk…
We discuss risk measures representing the minimum amount of capital a financial institution needs to raise and invest in a pre-specified eligible asset to ensure it is adequately capitalized. Most of the literature has focused on…
We study the feasibility and noise sensitivity of portfolio optimization under some downside risk measures (Value-at-Risk, Expected Shortfall, and semivariance) when they are estimated by fitting a parametric distribution on a finite sample…
Maximum drawdown, the largest cumulative loss from peak to trough, is one of the most widely used indicators of risk in the fund management industry, but one of the least developed in the context of measures of risk. We formalize drawdown…
The joint Value at Risk (VaR) and expected shortfall (ES) quantile regression model of Taylor (2017) is extended via incorporating a realized measure, to drive the tail risk dynamics, as a potentially more efficient driver than daily…
This paper investigates risk measures derived from the expected maximum deficit in a continuous-time framework and develops optimal reserve allocation strategies across multiple lines of business. We formalize the expected maximum deficit…
We derive new approximations for the Value at Risk and the Expected Shortfall at high levels of loss distributions with positive skewness and excess kurtosis, and we describe their precisions for notable ones such as for exponential, Pareto…
We establish strong duality relations for functional two-step compositional risk-constrained learning problems with multiple nonconvex loss functions and/or learning constraints, regardless of nonconvexity and under a minimal set of…
Under the continuous assumption on the generator $g$, Briand et al. [Electron. Comm. Probab. 5 (2000) 101--117] showed some connections between $g$ and the conditional $g$-expectation $({\mathcal{E}}_g[\cdot|{\mathcal{F}}_t])_{t\in[0,T]}$…
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…
In this paper, we present an algorithm for minimizing the difference between two submodular functions using a variational framework which is based on (an extension of) the concave-convex procedure [17]. Because several commonly used metrics…
A joint conditional autoregressive expectile and Expected Shortfall framework is proposed. The framework is extended through incorporating a measurement equation which models the contemporaneous dependence between the realized measures and…
Given measurements from sensors and a set of standard forces, an optimization based approach to identify weakness in structures is introduced. The key novelty lies in letting the load and measurements to be random variables. Subsequently…
De Finetti's optimal reinsurance is a set of contracts, one for each risk in a portfolio, that caps the retained aggregate variance to a pre-specified level while minimizing total expected loss. The premiums are determined using the…
In this paper, we refine and generalize closed forms for worst-case law invariant convex risk measures with uncertainty sets based on: i) closed balls under $p$-norms and Wasserstein distance; and ii) moment constraints involving mean and…