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Azzalini & Dalla Valle (1996) have recently discussed the multivariate skew-normal distribution which extends the class of normal distributions by the addition of a shape parameter. The first part of the present paper examines further…
Mixtures of generalized normal distributions (MGND) have gained popularity for modelling datasets with complex statistical behaviours. However, the estimation of the shape parameter within the maximum likelihood framework is quite complex,…
In this paper we show how to relate European call and put options on multiple assets to certain convex bodies called lift zonoids. Based on this, geometric properties can be translated into economic statements and vice versa. For instance,…
This PhD Thesis presents an investigation into the analysis of financial returns using mixture models, focusing on mixtures of generalized normal distributions (MGND) and their extensions. The study addresses several critical issues…
Gaussian graphical models are used throughout the natural sciences, social sciences, and economics to model the statistical relationships between variables of interest in the form of a graph. We here provide a pedagogic introduction to…
Recent developments in extreme value statistics have established the so-called geometric approach as a powerful modelling tool for multivariate extremes. We tailor these methods to the case of spatial modelling and examine their efficacy at…
This study presents a long-term alternative formula for stock price variation described by a geometric Brownian motion on the basis of median instead of mean or expected values. The proposed method is motivated by the observation made in…
Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit…
This article is the second one in a series on the use of scaling invariance in finance. In the first article (cond-mat/9906048), we introduced a new formalism for the pricing of derivative securities, which focusses on tradable objects…
The geometric mean of two matrices is considered and analyzed from a computational viewpoint. Some useful theoretical properties are derived and an analysis of the conditioning is performed. Several numerical algorithms based on different…
Learning the parameters of a (potentially partially observable) random field model is intractable in general. Instead of focussing on a single optimal parameter value we propose to treat parameters as dynamical quantities. We introduce an…
Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized…
We consider the problem of multi-task learning in the high dimensional setting. In particular, we introduce an estimator and investigate its statistical and computational properties for the problem of multiple connected linear regressions…
In this paper we consider several continuous-time multivariate non-Gaussian models applied to finance and proposed in the literature in the last years. We study the models focusing on the parsimony of the number of parameters, the…
We present here a general framework, expressed by a system of nonlinear differential equations, suitable for the modelling of taxation and redistribution in a closed (trading market) society. This framework allows to describe the evolution…
The upper tail of a claim size distribution of a property line of business is frequently modelled by Pareto distribution. However, the upper tail does not need to be Pareto distributed, extraordinary shapes are possible. Here, the…
The g-and-k and (generalised) g-and-h distributions are flexible univariate distributions which can model highly skewed or heavy tailed data through only four parameters: location and scale, and two shape parameters influencing the skewness…
Auxiliary variable is extensively used in survey sampling to improve the precision of estimates. Whenever there is availability of auxiliary information, we want to utilize it in the method of estimation to obtain the most efficient…
We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the…
Financial econometrics has become an increasingly popular research field. In this paper we review a few parametric and nonparametric models and methods used in this area. After introducing several widely used continuous-time and…