Max-stable models for multivariate extremes

Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models for univariate and multivariate extremes. A comprehensive account is given of the various ways in which max-stable models are described. Furthermore, a construction device is proposed for generating parametric families of max-stable distributions. Although the device is not new, its role as a model generator seems not yet to have been fully exploited.Comment: Invited paper for RevStat Statistical Journal. 22 pages, 3 figure

A short note on the problematic concept of excess demand in asset pricing models with mean-variance optimization

Referring to asset pricing models where demand is proportional to excess returns and said to be derived from a mean-variance optimization problem, the note formulates what probably is common knowledge but hardly ever made an explicit subject of discussion. This is an insufficient distinction between the desired holding of the risky asset on the part of the speculative agents, which is the solution to the optimization problem and usually directly presented as excess demand, and the desired change in this holding, which is what should reasonably constitute the excess demand on the market. The note arrives at the conclusion that in models with a market maker the story of the maximization of expected wealth should be dropped

Investigating dynamic dependence using copulae

A general methodology for time series modelling is developed which works down from distributional properties to implied structural models including the standard regression relationship. This general to specific approach is important since it can avoid spurious assumptions such as linearity in the form of the dynamic relationship between variables. It is based on splitting the multivariate distribution of a time series into two parts: (i) the marginal unconditional distribution, (ii) the serial dependence encompassed in a general function , the copula. General properties of the class of copula functions that fulfill the necessary requirements for Markov chain construction are exposed. Special cases for the gaussian copula with AR(p) dependence structure and for archimedean copulae are presented. We also develop copula based dynamic dependency measures — auto-concordance in place of autocorrelation. Finally, we provide empirical applications using financial returns and transactions based forex data. Our model encompasses the AR(p) model and allows non-linearity. Moreover, we introduce non-linear time dependence functions that generalize the autocorrelation function

Multi-asset minority games

We study analytically and numerically Minority Games in which agents may invest in different assets (or markets), considering both the canonical and the grand-canonical versions. We find that the likelihood of agents trading in a given asset depends on the relative amount of information available in that market. More specifically, in the canonical game players play preferentially in the stock with less information. The same holds in the grand canonical game when agents have positive incentives to trade, whereas when agents payoff are solely related to their speculative ability they display a larger propensity to invest in the information-rich asset. Furthermore, in this model one finds a globally predictable phase with broken ergodicity