The aim of this paper is to propose a convex risk measure in the framework of fuzzy random theory and verify its advantage over the conventional variance approach. For this purpose, this paper defines the quadratic deviation (QD) of fuzzy random variable as the mathematical expectation of QDs of fuzzy variables. As a result, the new risk criterion essentially describes the variation of a fuzzy ...

We derive bounds on the variance of a random variable in terms of its arithmetic and harmonic means. Both discrete and continuous cases are considered, and an operator version is obtained. Some refinements of the Kantorovich inequality are obtained. Bounds for the largest and smallest eigenvalues of a positive definite matrix are also obtained.

We consider a GI=G=1 queue in which the service time distribution and/or the interarrival time distribution has a heavy tail, i.e., a tail behaviour like t ? with 1 < 2, so that the mean is nite but the variance is innnite. We prove a heavy-traac limit theorem for the distribution of the stationary waiting time W. If the tail of the service time distribution is heavier than that of the interarr...

Meyer (1987) extended the theory of mean-variance criterion to include the comparison among distributions that differ only by location and scale parameters and to include general utility functions with only convexity or concavity restrictions. In this paper, we make some comments on Meyer’s paper and extend the results from Tobin (1958) that the indifference curve is convex upwards for risk ave...

We study the optimal portfolio selected by an investor who conforms to Siniscalchi (2009)’s Vector Expected Utility’s (VEU) axioms and who is ambiguity averse. To this end, we derive a mean-variance preference generalised to ambiguity from the second-order Taylor-Young expansion of the VEU certainty equivalent. We apply this Mean Variance Variability preference to the static two-assets portfoli...

5 We compare optimal liquidation policies in continuous time in the presence of trading impact using 6 numerical solutions of Hamilton Jacobi Bellman (HJB) partial differential equations (PDE). In par7 ticular, we compare the time-consistent mean-quadratic-variation strategy with the time-inconsistent 8 (pre-commitment) mean-variance strategy. We show that the two different risk measures lead t...

This paper suggests a simple method of deriving nonparametric lower bounds of the accuracy of statistical inference on heavy-tailed distributions. We present lower bounds of the mean squared error of the tail index, the tail constant, and extreme quantiles estimators. The results show that the normalizing sequences of robust estimators must depend in a specific way on the tail index and the tai...