A flexible framework for the analysis of tail events is proposed. The framework contains tail moment measures that allow for Expected Shortfall (ES) estimation. Connecting the implied tail thickness of a family of distributions with the quantile and expectile estimation, a platform for risk...

We define risk spillover as the dependence of a given asset variance on the past covariances and variances of other assets. Building on this idea, we propose the use of a highly flexible and tractable model to forecast the volatility of an international equity portfolio. According to the risk...

We introduce a measure of diversification for portfolios comprising d risky assets. This measure relates the smallest possible return variance among these d assets to the overall portfolio return variance, yielding the portion of non-diversifiable risk. In the context of normally distributed...

Sharpe ratio has been widely used in the portfolio management industry as well as fund industry (Robertson, 2001; Scholz and Wilkens, 2005). Users often forget the main core assumption describing the appropriateness of such risk-adjusted performance measure, namely asset return normality. This...

Portfolio risk estimation in volatile markets requires employing fat-tailed models for financial returns combined with copula functions to capture asymmetries in dependence and an appropriate downside risk measure. In this survey, we discuss how these three essential components can be combined...

Within the context of risk integration, we introduce in risk measurement stochastic holding period (SHP) models. This is done in order to obtain a 'liquidity-adjusted risk measure' characterized by the absence of a fixed time horizon. The underlying assumption is that - due to changes on market...

We propose and backtest a multivariate Value-at-Risk model for financial returns based on Tukey's g-and-h distribution. This distributional assumption is especially useful if (conditional) asymmetries as well as heavy tails have to be considered and fast random sampling is of importance. To...

Probabilistic preference models predict that a subject makes different choices with different probabilities in repeatedly experiments with the same stimuli. This paper explains why. First, we prove that a gamble is a statistical ensemble or sample function of a random field with canonical...

For the first time in the literature, this paper extends the CCAPM to establish the empirical relations between equity premia and state-dependent consumption and market risks. These relations are derived from a flexible, yet tractable, mixture distribution admitting the existence of two regimes,...

Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a number of risk measures that are of the form of ratios,...