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Systemic risk refers to the risk that the financial system is susceptible to failures due to the characteristics of the system itself. The tremendous cost of systemic risk requires the design and implementation of tools for the efficient…
We discuss equivalent axiomatic characterizations of distortion risk measures, and give a novel and concise proof of the characterization of elicitable distortion risk measures. Elicitability has recently been discussed as a desirable…
The risk of a financial position is usually summarized by a risk measure. As this risk measure has to be estimated from historical data, it is important to be able to verify and compare competing estimation procedures. In statistical…
In recent years, it has become apparent that an isolated microprudential approach to capital adequacy requirements of individual institutions is insufficient. It can increase the homogeneity of the financial system and ultimately the cost…
The family of admissible positions in a transaction costs model is a random closed set, which is convex in case of proportional transaction costs. However, the convexity fails, e.g. in case of fixed transaction costs or when only a finite…
Any solvency regime for financial institutions should be aligned with the fundamental objectives of regulation: protecting liability holders and securing the stability of the financial system. The first objective leads to consider…
A one-to-one correspondence is drawn between law invariant risk measures and divergences, which we define as functionals of pairs of probability measures on arbitrary standard Borel spaces satisfying a few natural properties. Divergences…
We propose a multivariate extension of a well-known characterization by S. Kusuoka of regular and coherent risk measures as maximal correlation functionals. This involves an extension of the notion of comonotonicity to random vectors…
Credit ratings are widely used by investors as a screening device. We introduce and study several natural notions of risk consistency that promote prudent investment decisions in the framework of Choquet rating criteria. Three closely…
In this paper, we provide a new property of value at risk (VaR), which is a standard risk measure that is widely used in quantitative financial risk management. We show that the subadditivity of VaR for given loss random variables holds for…
We establish structural properties of optimal stopping problems under time-consistent dynamic (coherent) risk measures, focusing on value function monotonicity and the existence of control limit (threshold) optimal policies. While such…
We present some formal properties of (symmetrical) commutativity, the major criterion used in transactional systems, which allow us to fully understand its advantages and disadvantages. The main result is that commutativity is subject to…
We develop a statistical framework for risk estimation, inspired by the axiomatic theory of risk measures. Coherent risk estimators -- functionals of P\&L samples inheriting the economic properties of risk measures -- are defined and…
We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature…
We consider active learning under incentive compatibility constraints. The main application of our results is to economic experiments, in which a learner seeks to infer the parameters of a subject's preferences: for example their attitudes…
We consider the risk sharing problem for capital requirements induced by capital adequacy tests and security markets. The agents involved in the sharing procedure may be heterogeneous in that they apply varying capital adequacy tests and…
In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage…
We consider a group consisting of N business units. We suppose there are regulatory constraints for each unit, more precisely, the net worth of each business unit is required to belong to a set of acceptable risks, assumed to be a convex…
The purpose of this paper is to utilize statistical methodologies to infer from market prices of assets and their derivatives the magnitude of the set of a measure M that defines acceptance sets of risky future cash flows. Specifically, we…
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…