Related papers: On the Dual Representation of Coherent Risk Measur…
The relationship between set-valued risk measures for processes and vectors on the optional filtration is investigated. The equivalence of risk measures for processes and vectors and the equivalence of their penalty function formulations…
Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We…
Mean-deviation models, along with the existing theory of coherent risk measures, are well studied in the literature. In this paper, we characterize monotonic mean-deviation (risk) measures from a general mean-deviation model by applying a…
We use the theory of coherent measures to look at the problem of surplus sharing in an insurance business. The surplus share of an insured is calculated by the surplus premium in the contract. The theory of coherent risk measures and the…
Probabilistic control design is founded on the principle that a rational agent attempts to match modelled with an arbitrary desired closed-loop system trajectory density. The framework was originally proposed as a tractable alternative to…
The financial crisis has dramatically demonstrated that the traditional approach to apply univariate monetary risk measures to single institutions does not capture sufficiently the perilous systemic risk that is generated by the…
The estimation of risk measures recently gained a lot of attention, partly because of the backtesting issues of expected shortfall related to elicitability. In this work we shed a new and fundamental light on optimal estimation procedures…
In this paper, we introduce a new class of set-valued risk measures, named set-valued star-shaped risk measures. Motivated by the results of scalar monetary and star-shaped risk measures, this paper investigates the representation theorems…
In this paper, we consider continuous-time stochastic optimal control problems where the cost is evaluated through a coherent risk measure. We provide an explicit gradient descent-ascent algorithm which applies to problems subject to…
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…
In this work we present two particular cases of the general duality result for linear optimisation problems over signed measures with infinitely many constraints in the form of integrals of functions with respect to the decision variables…
This paper gives an overview of the theory of dynamic convex risk measures for random variables in discrete time setting. We summarize robust representation results of conditional convex risk measures, and we characterize various time…
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…
In this research, starting from a widely accepted definition of risk, we support the idea that risk reduction is a more realistic objective than risk minimization, which represents a theoretical utopia. Furthermore, significant risk…
We review the nature of some well-known phenomena such as volatility smiles, convexity adjustments and parallel derivative markets. We propose that the market is incomplete and postulate the existence of intrinsic risks in every contingent…
Complex risk is a critical factor for both intelligent systems and risk management. In this paper, we consider a special class of risk statistics, named complex risk statistics. Our result provides a new approach for addressing complex…
Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of…
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…
In this paper monetary risk measures that are positively superhomogeneous, called star-shaped risk measures, are characterized and their properties studied. The measures in this class, which arise when the controversial subadditivity…
Procyclicality of historical risk measure estimation means that one tends to over-estimate future risk when present realized volatility is high and vice versa under-estimate future risk when the realized volatility is low. Out of it…