In this paper we model the daily average temperature via an extended version of the standard Ornstein Uhlenbeck process driven by a Levy noise with seasonally adjusted asymmetric ARCH process for volatility. More precisely, we model the disturbances with the Normal inverse Gaussian (NIG) and...

The bounds for risk measures of a portfolio when its components have known marginal distributions but the dependence among the risks is unknown are often too wide to be useful in practice. Moreover, availability of additional dependence information, such as knowledge of some higher-order...

We show that maximizing distortion risk measures over the set of distribution functions with given mean is equivalent to maximizing their concave counterpart. In the case of Value-at-Risk and Tail Value-at-Risk the equivalence also holds when adding information on higher moments

We study the impact of dependence uncertainty on E(X_1X_2 · · · X_d) when X_i ∼ F_i for all i. Under some conditions on the Fi, explicit sharp bounds are obtained and a numerical method is provided to approximate them for arbitrary choices of the F_i. The results are applied to assess the...

We study upper and lower bounds on the expectile risk measure of risky portfolios when the joint distribution of the risky components is not fully specified. First, we summarize methods for obtaining bounds when only the marginal distributions of the components are known, but not their...