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In structural credit risk models, default events and the ensuing losses are both derived from the asset values at maturity. Hence it is of utmost importance to choose a distribution for these asset values which is in accordance with…
We investigate to which extent the relevant features of (static) Systemic Risk Measures can be extended to a conditional setting. After providing a general dual representation result, we analyze in greater detail Conditional Shortfall…
The intuition of risk is based on two main concepts: loss and variability. In this paper, we present a composition of risk and deviation measures, which contemplate these two concepts. Based on the proposed Limitedness axiom, we prove that…
We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a "composable constraint encoding". We show that every composable constraint encoding…
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…
We introduce the notion of an accessible $\infty$-cosmos and prove that these include the basic examples of $\infty$-cosmoi and are stable under the main constructions. A consequence is that the vast majority of known examples of…
This paper studies an $\alpha$-robust utility maximization problem where an investor faces an intractable claim -- an exogenous contingent claim with known marginal distribution but unspecified dependence structure with financial market…
This paper develops a unified framework for the robustification of risk measures beyond the classical convex and cash-additive setting. We consider general risk measures on Lp spaces and construct their robust counterparts through families…
Comonotonicity (``same variation'') of random variables minimizes hedging possibilities and has been widely used, e.g., in Gilboa and Schmeidler's ambiguity models. This paper investigates anticomonotonicity (``opposite variation'';…
We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the…
Portfolio diversification is a cornerstone of modern finance, while risk aversion is central to decision theory; both concepts are long-standing and foundational. We investigate their connections by studying how different forms of…
We address the problem of sharing risk among agents with preferences modelled by a general class of comonotonic additive and law-based functionals that need not be either monotone or convex. Such functionals are called distortion…
This paper is the continuation of "Pricing with coherent risk" and deals with further applications of coherent risk measures to problems of finance. First, we study the optimization problem. Three forms of this problem are considered.…
Resource adequacy studies typically use standard metrics such as Loss of Load Expectation and Expected Energy Unserved to quantify the risk of supply shortfalls. This paper critiques present approaches to adequacy assessment and capacity…
Although the CML (Capital Market Line), the Intertemporal-CAPM, the CAPM/SML (Security Market Line) and the Intertemporal Arbitrage Pricing Theory (IAPT) are widely used in portfolio management, valuation and capital markets financing;…
Pivotal within quantum physics, the concept of quantum incompatibility is generally related to algebraic aspects of the formalism, such as commutation relations and unbiasedness of bases. Recently, the concept was identified as a resource…
To achieve robustness of risk across different assets, risk parity investing rules, a particular state of risk contributions, have grown in popularity over the previous few decades. To generalize the concept of risk contribution from the…
We characterize when a convex risk measure associated to a law-invariant acceptance set in $L^\infty$ can be extended to $L^p$, $1\leq p<\infty$, preserving finiteness and continuity. This problem is strongly connected to the statistical…
We show how risk measures originally defined in a model free framework in terms of acceptance sets and reference assets imply a meaningful underlying probability structure. Hereafter we construct a maximal domain of definition of the risk…
In this paper, we characterize compatibility of distributions and probability measures on a measurable space. For a set of indices $\mathcal J$, we say that the tuples of probability measures $(Q_i)_{i\in \mathcal J} $ and distributions…