Related papers: On the Dual Representation of Coherent Risk Measur…
We address the statistical estimation of composite functionals which may be nonlinear in the probability measure. Our study is motivated by the need to estimate coherent measures of risk, which become increasingly popular in finance,…
This paper compares two different frameworks recently introduced in the literature for measuring risk in a multi-period setting. The first corresponds to applying a single coherent risk measure to the cumulative future costs, while the…
Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set…
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…
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…
The equivalence between multiportfolio time consistency of a dynamic multivariate risk measure and a supermartingale property is proven. Furthermore, the dual variables under which this set-valued supermartingale is a martingale are…
The framework of this paper is that of risk measuring under uncertainty, which is when no reference probability measure is given. To every regular convex risk measure on ${\cal C}_b(\Omega)$, we associate a unique equivalence class of…
We give a complete characterization of both comonotone and not comonotone coherent risk measures in the discrete finite probability space, where each outcome is equally likely. To the best of our knowledge, this is the first work that…
Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative…
We establish a profound connection between coherent risk measures, a prominent object in quantitative finance, and uniform integrability, a fundamental concept in probability theory. Instead of working with absolute values of random…
We study coherent risk measures which are time-consistent for multiple filtrations. We show that a coherent risk measure is time-consistent for every filtration if and only if it is one of four main types. Furthermore, if the risk measure…
We introduce set risk measures (SRMs), real-valued maps defined on the family of non-empty closed bounded sets of essentially bounded random variables. SRMs extend traditional scalar risk measures by assigning a single capital requirement…
Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to quantify the acceptable risk, often in the…
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…
A risk analyst assesses potential financial losses based on multiple sources of information. Often, the assessment does not only depend on the specification of the loss random variable but also various economic scenarios. Motivated by this…
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…
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…
We present a general framework for measuring the liquidity risk. The theoretical framework defines a class of risk measures that incorporate the liquidity risk into the standard risk measures. We consider a one-period risk measurement…
Shortfall systemic (multivariate) risk measures $\rho$ defined through an $N$-dimensional multivariate utility function $U$ and random allocations can be represented as classical (one dimensional) shortfall risk measures associated to an…
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…