Statistical modelling of road accident data via graphical models and hierarchical Bayesian models.

The objective of this thesis is to develop statistical models for multivariate road accident data. Two directions of research are followed: graphical modelling for contingency tables cross-classified by accident characteristics, and hierarchical Bayesian models for multiple accident frequencies of different types modelled jointly. Multi-dimensional tables are analysed and it is shown how to use collapsibility to reduce the dimensionality of the analysis without the problems of Simpson's paradox. It is revealed that accident severity and the number of casualties are associated, and that these variables are mainly influenced by the number of vehicles and speed limit. Graphical chain models allow causal hypotheses to be formulated and it is shown how they are valuable tools for empirical research about road accident characteristics. The hierarchical Bayesian models developed combine generalized linear models with random effects. The novelty of these models consists in the joint modelling of multiple response variables. The models account for overdispersion and they are used for accident prediction and for ranking hazardous sites. All models are fully Bayesian and are fitted using Markov Chain Monte Carlo methods. It is shown that multiple response variables models are superior to separate univariate response models. Some theoretical problems are examined regarding the maximum likelihood estimation process for the two parameters negative binomial distribution. A condition is given that is equivalent with unique maximum likelihood estimators. The two directions of research are connected by using graphs to describe the models. In addition, a new Bayesian model selection procedure for contingency tables is proposed. This is based on Gibbs sampling and avoids problems associated with asymptotic tests. The conclusions revealed here can help practitioners to design better safety policies and to spend money more wisely on sites that really are dangerous

Entropy Concepts Applied to Option Pricing

Uncertainty is one of the most important concept in financial mathematics applications. In this paper we review some important aspects related to the application of entropy-related concepts to option pricing. The Kullback-Leibler information divergence and the informational energy introduced by Onicescu are the main tools investigated in this paper. We highlight a necessary condition that must be verified when obtaining the probability distribution minimising the Kullback-Leibler information divergence. Deriving a probability distribution by optimising the information energy has some pitfalls that are discussed in this paper

Estimation functions and uniformly most powerful tests for inverse Gaussian distribution

summary:The aim of this article is to develop estimation functions by confidence regions for the inverse Gaussian distribution with two parameters and to construct tests for hypotheses testing concerning the parameter $\lambda$ when the mean parameter $\mu$ is known. The tests constructed are uniformly most powerful tests and for testing the point null hypothesis it is also unbiased

Cross hedging jet fuel on the Singapore spot market.

In this paper we test for the most effective cross hedging instrument for the Singapore spot market in jet fuel over the period February 4, 1997 to August 21, 2001. Our results are mixed. We find that the heating oil contract is the best in-sample cross-hedging instrument. It has the highest correlation with the spot price and gives the best regression results. However, after correcting for serial correlation, the goodness of fit measured by R2 is rather low. Out of sample results are weak for all models and ambiguous with respect to the heating oil contract

A factor model for joint default probabilities. Pricing of CDS, index swaps and index tranches

A factor model is proposed for the valuation of credit default swaps, credit indices and CDO contracts. The model of default is based on the first-passage distribution of a Brownian motion time modified by a continuous time-change. Various model specifications fall under this general approach based on defining the credit-quality process as an innovative time-change of a standard Brownian motion where the volatility process is mean reverting Lévy driven OU type process. Our models are bottom-up and can account for sudden moves in the level of CDS spreads representing the so-called credit gap risk. We develop FFT computational tools for calculating the distribution of losses and we show how to apply them to several specifications of the time-changed Brownian motion. Our line of modelling is flexible enough to facilitate the derivation of analytical formulae for conditional probabilities of default and prices of credit derivatives