Related papers: Intrinsic risk measures
In normal times, it is assumed that financial institutions operating in non-overlapping sectors have complementary and distinct outcomes, typically reflected in mostly uncorrelated outcomes and asset returns. Such is the reasoning behind…
We describe a general framework for measuring risks, where the risk measure takes values in an abstract cone. It is shown that this approach naturally includes the classical risk measures and set-valued risk measures and yields a natural…
The gain-loss ratio is known to enjoy very good properties from a normative point of view. As a confirmation, we show that the best market gain-loss ratio in the presence of a random endowment is an acceptability index and we provide its…
We consider the problem of governing systemic risk in a banking system model. The banking system model consists in an initial value problem for a system of stochastic differential equations whose dependent variables are the log-monetary…
Systemic risk is the risk that a company- or industry-level risk could trigger a huge collapse of another or even the whole institution. Various systemic risk measures have been proposed in the literature to quantify the domino and…
Geometrically convex functions constitute an interesting class of functions obtained by replacing the arithmetic mean with the geometric mean in the definition of convexity. As recently suggested, geometric convexity may be a sensible…
Managing a portfolio to a risk model can tilt the portfolio toward weaknesses of the model. As a result, the optimized portfolio acquires downside exposure to uncertainty in the model itself, what we call "second order risk." We propose a…
A method for calculating multi-portfolio time consistent multivariate risk measures in discrete time is presented. Market models for $d$ assets with transaction costs or illiquidity and possible trading constraints are considered on a…
Measuring the contribution of a bank or an insurance company to overall systemic risk is a key concern, particularly in the aftermath of the 2007--2009 financial crisis and the 2020 downturn. In this paper, we derive worst-case and…
Conditional forecasts of risk measures play an important role in internal risk management of financial institutions as well as in regulatory capital calculations. In order to assess forecasting performance of a risk measurement procedure,…
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…
This paper studies a Kyle-Back model with a risk-averse insider possessing exponential utility and a dynamic stochastic signal about the asset's terminal fundamental value. While the existing literature considers either risk-neutral…
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…
By adopting a distributional viewpoint on law-invariant convex risk measures, we construct dynamics risk measures (DRMs) at the distributional level. We then apply these DRMs to investigate Markov decision processes, incorporating latent…
The mathematical problem concerning intrinsic storage optimisation is formulated and solved by means of variational analysis. The solution, though obtained in implicit form, still sheds light on many important features of the optimal…
We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control…
In a capital adequacy framework, risk measures are used to determine the minimal amount of capital that a financial institution has to raise and invest in a portfolio of pre-specified eligible assets in order to pass a given capital…
We study risk sharing among agents with preferences modeled by heterogeneous distortion risk measures, who are not necessarily risk averse. Pareto optimality for agents using risk measures is often studied through the lens of…
Motivated by the results of static monetary or star-shaped risk measures, the paper investigates the representation theorems in the dynamic framework. We show that dynamic monetary risk measures can be represented as the lower envelope of a…
Our paper contributes to the theory of conditional risk measures and conditional certainty equivalents. We adopt a random modular approach which proved to be effective in the study of modular convex analysis and conditional risk measures.…