Related papers: On the link between monetary and star-shaped risk …
Building on the one-to-one relationship between generalized FGM copulas and multivariate Bernoulli distributions, we prove that the class of multivariate distributions with generalized FGM copulas is a convex polytope. Therefore, we find…
This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…
We address the problem that classical risk measures may not detect the tail risk adequately. This can occur for instance due to averaging when calculating the Expected Shortfall. The current literature proposes the so-called adjusted…
The minimality of the penalization function associated with a convex risk measure is analyzed in this paper. First, in a general static framework, we provide necessary and sufficient conditions for a penalty function defined in a convex and…
This paper is mainly a survey of recent research developments regarding methods for risk minimization in financial markets modeled by It\^o-L\'evy processes, but it also contains some new results on the underlying stochastic maximum…
This paper was presented and written for two seminars: a national UK University Risk Conference and a Risk Management industry workshop. The target audience is therefore a cross section of Academics and industry professionals. The current…
In the second part of our series we suggest new definitions of credit bond duration and convexity that remain consistent across all levels of credit quality including deeply distressed bonds and introduce additional risk measures that are…
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…
A risk-neutral method is always used to price and hedge contingent claims in complete market, but another method based on utility maximization or risk minimization is wildly used in more general case. One can find all kinds of special risk…
We study a static portfolio optimization problem with two risk measures: a principle risk measure in the objective function and a secondary risk measure whose value is controlled in the constraints. This problem is of interest when it is…
In this paper we present a theoretical framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures, and we establish a duality between them. We…
Under the continuous assumption on the generator $g$, Briand et al. [Electron. Comm. Probab. 5 (2000) 101--117] showed some connections between $g$ and the conditional $g$-expectation $({\mathcal{E}}_g[\cdot|{\mathcal{F}}_t])_{t\in[0,T]}$…
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…
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 propose a risk measurement approach for a risk-averse stochastic problem. We provide results that guarantee that our problem has a solution. We characterize and explore the properties of the argmin as a risk measure and the minimum as a…
Rates of convergence for empirical risk minimizers have been well studied in the literature. In this paper, we aim to provide a complementary set of results, in particular by showing that after normalization, the risk of the empirical…
Equivalent characterizations of multiportfolio time consistency are deduced for closed convex and coherent set-valued risk measures on $L^p(\Omega,\mathcal F, P; R^d)$ with image space in the power set of $L^p(\Omega,\mathcal F_t,P;R^d)$.…
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…
Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been…
In this paper we introduce a generalization of classical risk measures in which the risk is represented by a step function taking two values, corresponding to two endogenously determined market regimes. This extends the traditional…