Assuming the time series of random returns to be jointly elliptical, we derive a relationship between its conditional variance and the probability density function of the conditioning set. In the case that such a relationship is linear in a quadratic form for of the conditioning variables, we...

Sequential maximum likelihood and GMM estimators of distributional parameters obtained from the standardised innovations of multivariate conditionally heteroskedastic dynamic regression models evaluated at Gaussian PML estimators preserve the consistency of mean and variance parameters while...

Several approaches exist to model decision making under risk, where risk can be broadly defined as the effect of variability of random outcomes. One of the main approaches in the practice of decision making under risk uses mean-risk models; one such well-known is the classical Markowitz model,...

In this paper portfolio problems with linear loss functions and multivariate elliptical distributed returns are studied. We consider two risk measures, Value-at-Risk and Conditional-Value-at-Risk, and two types of decision makers, risk neutral and risk averse. For Value-at-Risk, we show that the...

We discuss a class of risk measures for portfolio optimization with linear loss functions, where the random returns of financial instruments have a multivariate elliptical distribution. Under this setting we pay special attention to two risk measures, Value-at-Risk and Conditional-Value-at-Risk...

Idiosyncratic security risks are modelled as following a joint spherical distribution characterized by a mean vector and a generalized covariance matrix. Skewness is generated by a single factor for the whole economy, but upon which different securities have different loadings. This results in...