based on credibilistic value-at-risk (cvar) of regularfuzzy variable, we introduce a new cvar reduction method fortype-2 fuzzy variables. the reduced fuzzy variables arecharacterized by parametric possibility distributions. we establishsome useful analytical expressions for mean values and secondorder moments of common reduced fuzzy variables. the convex properties of second order moments with ...

This paper studies three notions of fuzzy dominance based on credibility measure, namely, the fuzzy mean-risk dominance, the first credibilistic dominance and the second credibilistic dominance. More precisely, we introduce and examine some properties of the Fuzzy Lower Partial Moments (FLPM) of a fuzzy variable and, we deduce the Fuzzy Kappa index (FK) of a fuzzy variable, that is, a riskadjus...

investors use different approaches to select optimal portfolio. so, optimal investment choices according to return can be interpreted in different models. the traditional approach to allocate portfolio selection called a mean - variance explains. another approach is markov chain. markov chain is a random process without memory. this means that the conditional probability distribution of the nex...

An investigation of the limiting behavior of a risk capital allocation rule based on the Conditional Tail Expectation (CTE) risk measure is carried out. More specifically, with the help of general notions of Extreme Value Theory (EVT), the aforementioned risk capital allocation is shown to be asymptotically proportional to the corresponding Value-at-Risk (VaR) risk measure. The existing methodo...

The modeling of complex risk situations imposes the existence of multiple ways to represent the risk and compare the risk situations between them. In probabilistic models, risk is described by random variables and risk situations are compared by stochastic dominance. In possibilistic or credibilistic models, risk is represented by fuzzy variables. This paper concerns three indicators of dominan...

Recent literature has investigated the risk aggregation of a portfolio X = (Xi)1≤i≤n under the sole assumption that the marginal distributions of the risks Xi are specified but not their dependence structure. There exists a range of possible values for any risk measure of S = ∑n i=1Xi and the dependence uncertainty spread, as measured by the difference between the upper bound and the lower boun...

A distortion risk measure used in finance and insurance is defined as the expected value of potential loss under a scenario probability measure. In this paper, the tail distortion risk measure is introduced to assess tail risks of excess losses modeled by the right tails of loss distributions. The asymptotic linear relation between tail distortion and Value-at-Risk is derived for heavy tailed l...

Starting with a time-0 coherent risk measure defined for “value processes”, we also define risk measurement processes. Two other constructions of measurement processes are given in terms of sets of test probabilities. These latter constructions are identical and are related to the former construction when the sets fulfill a stability condition also met in multiperiod treatment of ambiguity as i...

Evaluating risk measures, premiums, and capital allocation based on dependent multi-losses is a notoriously difficult task. In this paper, we demonstrate how this can be successfully accomplished when losses follow the multivariate Pareto distribution of the second kind, which is an attractive model for multi-losses whose dependence and tail heaviness are influenced by a heavy-tailed background...