New framework reveals global warming’s impact on risk that multiple regions experience hot and dry conditions simultaneously.

In this paper, we perform Bayesian inference and prediction for a GARCH model where the innovations are assumed to follow a mixture of two Gaussian distributions. This GARCH model can capture the patterns usually exhibited by many financial time series such as volatility clustering, large kurtosis and extreme observations. A Griddy-Gibbs sampler implementation is proposed for parameter estimation and volatility prediction. The method is illustrated using the Swiss Market Index. Keywords AbstractIn this paper, we perform Bayesian inference and prediction for a GARCH model where the innovations are assumed to follow a mixture of two Gaussian distributions. This GARCH model can capture the patterns usually exhibited by many financial time series such as volatility clustering, large kurtosis and extreme observations. A Griddy-Gibbs sampler implementation is proposed for parameter estimation and volatility prediction. The method is illustrated using the Swiss Market Index.

A time-varying risk analysis is proposed for an adaptive design framework in nonstationary conditions arising from climate change. A Bayesian, dynamic conditional copula is developed for modeling the time-varying dependence structure between mixed continuous and discrete multiattributes of multidimensional hydrometeorological phenomena. Joint Bayesian inference is carried out to fit the marginals and copula in an illustrative example using an adaptive, Gibbs Markov Chain Monte Carlo (MCMC) sampler. Posterior mean estimates and credible intervals are provided for the model parameters and the Deviance Information Criterion (DIC) is used to select the model that best captures different forms of nonstationarity over time. This study also introduces a fully Bayesian, time-varying joint return period for multivariate timedependent risk analysis in nonstationary environments. The results demonstrate that the nature and the risk of extreme-climate multidimensional processes are changed over time under the impact of climate change, and accordingly the long-term decision making strategies should be updated based on the anomalies of the nonstationary environment.

This paper deals with the analysis of temporal dependence in multivariate time series. The dependence structure between the marginal series is modelled through the use of copulas which, unlike the correlation matrix, give a complete description of the joint distribution. The parameters of the copula function vary through time following certain evolution equations depending on their previous values and the historical data. The marginal time series follow standard univariate GARCH models. We develop full Bayesian inference where the whole set of model parameters is estimated simultaneously. This represents an essential difference with previous approaches in the literature where the marginal and the copula parameters are estimated separately in two consecutive steps. Moreover, we propose a Bayesian procedure for the estimation of the Value-at-Risk (VaR) of a portfolio of assets, providing point estimates and predictive intervals. The proposed copula model allows us to capture the dependence structure between the individual assets which strongly influences the portfolio VaR. Finally, we also address the problem of optimal portfolio selection based on the estimation of mean-VaR efficient frontiers.The proposed approach is illustrated with simulated and real financial time series.

This paper describes a Bayesian approach to make inference for risk reserve processes with an unknown claim-size distribution. A flexible model based on mixtures of Erlang distributions is proposed to approximate the special features frequently observed in insurance claim sizes, such as long tails and heterogeneity. A Bayesian density estimation approach for the claim sizes is implemented using reversible jump Markov chain Monte Carlo methods. An advantage of the considered mixture model is that it belongs to the class of phase-type distributions, and thus explicit evaluations of the ruin probabilities are possible. Furthermore, from a statistical point of view, the parametric structure of the mixtures of the Erlang distribution offers some advantages compared with the whole over-parametrized family of phase-type distributions. Given the observed claim arrivals and claim sizes, we show how to estimate the ruin probabilities, as a function of the initial capital, and predictive intervals that give a measure of the uncertainty in the estimations.