Related papers: Multivariate risk measures in the non-convex setti…

In risk theory, financial asset returns often follow heavy-tailed distributions. Investors and risk managers used to compare risk measures as the value at risk or tail value at risk in order over the whole confidence levels to avoid the…

In this paper we present results on scalar risk measures in markets with transaction costs. Such risk measures are defined as the minimal capital requirements in the cash asset. First, some results are provided on the dual representation of…

In this paper, we explore a static setting for the assessment of risk in the context of mathematical finance and actuarial science that takes into account model uncertainty in the distribution of a possibly infinite-dimensional risk factor.…

The variation distance closure of an exponential family with a convex set of canonical parameters is described, assuming no regularity conditions. The tools are the concepts of convex core of a measure and extension of an exponential…

This paper applies risk analysis to medical problems, through the properties of nonlinear responses (convex or concave). It shows 1) necessary relations between the nonlinearity of dose-response and the statistical properties of the…

This paper studies distributionally robust optimization for a rich class of risk measures with ambiguity sets defined by $\phi$-divergences. The risk measures are allowed to be non-linear in probabilities, are represented by Choquet…

Based on supermodularity ordering properties, we show that convex risk measures of credit losses are nondecreasing w.r.t. credit-credit and, in a wrong-way risk setup, credit-market, covariances of elliptically distributed latent factors.…

Recently, Castagnoli et al. (2021) introduce the class of star-shaped risk measures as a generalization of convex and coherent ones, proving that there is a representation as the pointwise minimum of some family composed by convex risk…

We consider a discrete-time model of a financial market where a risky asset is bought and sold with transactions having a transient price impact. It is shown that the corresponding utility maximization problem admits a solution. We manage…

In this paper, we consider the problem of hedging Asian options in financial markets with transaction costs. For this, we use the asymptotic hedging approach. The main task of asymptotic hedging in financial markets with transaction costs…

We give sufficient conditions for the expected excess and the upper semideviation of recourse functions to be strongly convex. This is done in the setting of two-stage stochastic programs with complete linear recourse and random right-hand…

We propose a route for the evaluation of risk based on a transformation of the covariance matrix. The approach uses a `potential' or `objective' function. This allows us to rescale data from different assets (or sources) such that each data…

Risk assessment under different possible scenarios is a source of uncertainty that may lead to concerning financial losses. We address this issue, first, by adapting a robust framework to the class of spectral risk measures. Second, we…

The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a…

The entropic value-at-risk (EVaR) is a new coherent risk measure, which is an upper bound for both the value-at-risk (VaR) and conditional value-at-risk (CVaR). As important properties, the EVaR is strongly monotone over its domain and…

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…

We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…

This paper presents an extension to the nonlinear Model Predictive Control for Tracking scheme able to guarantee convergence even in cases of non-convex output admissible sets. This is achieved by incorporating a convexifying homeomorphism…

Convex duality for two two different super--replication problems in a continuous time financial market with proportional transaction cost is proved. In this market, static hedging in a finite number of options, in addition to usual dynamic…

In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…