Related papers: Expected Shortfall: a natural coherent alternative…
We consider the problem of portfolio optimization in the presence of market impact, and derive optimal liquidation strategies. We discuss in detail the problem of finding the optimal portfolio under Expected Shortfall (ES) in the case of…
This paper describes an empirical study of shortfall optimization with Barra Extreme Risk. We compare minimum shortfall to minimum variance portfolios in the US, UK, and Japanese equity markets using Barra Style Factors (Value, Growth,…
A risk measure that is consistent with the second-order stochastic dominance and additive for sums of independent random variables can be represented as a weighted entropic risk measure (WERM). The expected utility maximization problem with…
We study the sensitivity to estimation error of portfolios optimized under various risk measures, including variance, absolute deviation, expected shortfall and maximal loss. We introduce a measure of portfolio sensitivity and test the…
The aim of this paper is to describe a new an integrated methodology for project control under uncertainty. This proposal is based on Earned Value Methodology and risk analysis and presents several refinements to previous methodologies.…
The risk of financial positions is measured by the minimum amount of capital to raise and invest in eligible portfolios of traded assets in order to meet a prescribed acceptability constraint. We investigate nondegeneracy, finiteness and…
Cr\'epey, Frikha, and Louzi (2025) introduced a nested stochastic approximation algorithm and its multilevel acceleration to compute the value-at-risk and expected shortfall of a random financial loss. We hereby establish central limit…
Under the Fundamental Review of the Trading Book (FRTB) capital charges for the trading book are based on the coherent expected shortfall (ES) risk measure, which show greater sensitivity to tail risk. In this paper it is argued that…
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…
Beta is a widely used quantity in investment analysis. We review the common interpretations that are applied to beta in finance and show that the standard method of estimation - least squares regression - is inconsistent with these…
We provide a new characterization of second-order stochastic dominance, also known as increasing concave order. The result has an intuitive interpretation that adding a risk with negative expected value in adverse scenarios makes the…
The hazard ratio, typically estimated using Cox's famous proportional hazards model, is the most common effect measure used to describe the association or effect of a covariate on a time-to-event outcome. In recent years the hazard ratio…
The instability of historical risk factor correlations renders their use in estimating portfolio risk extremely questionable. In periods of market stress correlations of risk factors have a tendency to quickly go well beyond estimated…
We consider in this paper some structured financial products, known as reverse convertible notes, that resulted in substantial losses to certain buyers of these notes in recent years. We shall focus on specific reverse convertible notes…
The paper concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be…
For some estimations and predictions, we solve minimization problems with asymmetric loss functions. Usually, we estimate the coefficient of regression for these problems. In this paper, we do not make such the estimation, but rather give a…
We propose a multilevel stochastic approximation (MLSA) scheme for the computation of the value-at-risk (VaR) and expected shortfall (ES) of a financial loss, which can only be computed via simulations conditionally on the realisation of…
We introduce a continuous-time framework for the prediction of outstanding liabilities, in which chain-ladder development factors arise as a histogram estimator of a cost-weighted hazard function running in reversed development time. We use…
We investigate the quantification of demographic risk in a framework consistent with the market-consistent valuation imposed by Solvency II. We provide compact formulas for evaluating inflows and outflows of a portfolio of insurance…
We study a space of coherent risk measures M_phi obtained as certain expansions of coherent elementary basis measures. In this space, the concept of ``Risk Aversion Function'' phi naturally arises as the spectral representation of each risk…