Related papers: Set-valued shortfall and divergence risk measures
In this paper, we consider a multi-objective control problem for stochastic systems that seeks to minimize a cost of interest while ensuring safety. We introduce a novel measure of safety risk using the conditional value-at-risk and a set…
Value adjustment of uncollateralized trades is determined within a risk-neutral pricing framework. When hedging such trades, investors cannot freely trade protection on their own name, thus facing an incomplete market. This fact is…
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…
Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic…
In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…
The purpose of this paper is to describe and extend the use of the newly-introduced measure, residual estimation risk. Following the seminal work of Bignozzi and Tsanakas, the quantification of residual estimation risk is proposed in a…
Utility-Based Shortfall Risk (UBSR) is a risk metric that is increasingly popular in financial applications, owing to certain desirable properties that it enjoys. We consider the problem of estimating UBSR in a recursive setting, where…
Systematic investment strategies are exposed to a subtle but pervasive vulnerability: the progressive erosion of their effectiveness as market regimes change. Traditional risk measures, designed to capture volatility or drawdowns, overlook…
Motivated by the asset-liability management of a nuclear power plant operator, we consider the problem of finding the least expensive portfolio, which outperforms a given set of stochastic benchmarks. For a specified loss function, the…
In the paper a problem of risk measures on a discrete-time market model with transaction costs is studied. Strategy effectiveness and shortfall risk is introduced. This paper is a generalization of quantile hedging presented in [4].
We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The…
The issue of model risk in default modeling has been known since inception of the Academic literature in the field. However, a rigorous treatment requires a description of all the possible models, and a measure of the distance between a…
We study the two-times differentiability of the value functions of the primal and dual optimization problems that appear in the setting of expected utility maximization in incomplete markets. We also study the differentiability of the…
This paper presents an optimal allocation problem in a financial market with one risk-free and one risky asset, when the market is driven by a stochastic market price of risk. We solve the problem in continuous time, for an investor with a…
Optimization of distortion riskmetrics with distributional uncertainty has wide applications in finance and operations research. Distortion riskmetrics include many commonly applied risk measures and deviation measures, which are not…
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…
Spectral risk objectives - also called $L$-risks - allow for learning systems to interpolate between optimizing average-case performance (as in empirical risk minimization) and worst-case performance on a task. We develop stochastic…
Volatility is the canonical measure of financial risk, a role largely inherited from Modern Portfolio Theory. Yet, its universality rests on restrictive efficiency assumptions that render volatility, at best, an incomplete proxy for true…
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…
In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk…