Bayesian estimation of ruin probabilities with heterogeneous and heavy-tailed insurance claim size distribution

This paper describes a Bayesian approach to make inference for risk reserve processes with 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 then, explicit evaluations of the ruin probabilities are possible. Furthermore, from a statistical point of view, the parametric structure of the mixtures of Erlang distribution others some advantages compared with the whole over-parameterized 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 which give a measure of the uncertainty in the estimations

Particle Learning and Smoothing

Particle learning (PL) provides state filtering, sequential parameter learning and smoothing in a general class of state space models. Our approach extends existing particle methods by incorporating the estimation of static parameters via a fully-adapted filter that utilizes conditional sufficient statistics for parameters and/or states as particles. State smoothing in the presence of parameter uncertainty is also solved as a by-product of PL. In a number of examples, we show that PL outperforms existing particle filtering alternatives and proves to be a competitor to MCMC.Comment: Published in at http://dx.doi.org/10.1214/10-STS325 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Measuring the vulnerability of the Uruguayan population to vector-borne diseases via spatially hierarchical factor models

We propose a model-based vulnerability index of the population from Uruguay to vector-borne diseases. We have available measurements of a set of variables in the census tract level of the 19 Departmental capitals of Uruguay. In particular, we propose an index that combines different sources of information via a set of micro-environmental indicators and geographical location in the country. Our index is based on a new class of spatially hierarchical factor models that explicitly account for the different levels of hierarchy in the country, such as census tracts within the city level, and cities in the country level. We compare our approach with that obtained when data are aggregated in the city level. We show that our proposal outperforms current and standard approaches, which fail to properly account for discrepancies in the region sizes, for example, number of census tracts. We also show that data aggregation can seriously affect the estimation of the cities vulnerability rankings under benchmark models.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS497 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Particle Learning for General Mixtures

This paper develops particle learning (PL) methods for the estimation of general mixture models. The approach is distinguished from alternative particle filtering methods in two major ways. First, each iteration begins by resampling particles according to posterior predictive probability, leading to a more efficient set for propagation. Second, each particle tracks only the "essential state vector" thus leading to reduced dimensional inference. In addition, we describe how the approach will apply to more general mixture models of current interest in the literature; it is hoped that this will inspire a greater number of researchers to adopt sequential Monte Carlo methods for fitting their sophisticated mixture based models. Finally, we show that PL leads to straight forward tools for marginal likelihood calculation and posterior cluster allocation.Business Administratio

Simulation-based sequential analysis of markov switching stochastic volatility models

Abstract We propose a simulation-based algorithm for inference in stochastic volatility models with possible regime switching in which the regime state is governed by a first-order Markov process. Using auxiliary particle filters we developed a strategy to sequentially learn about states and parameters of the model. The methodology is tested against a synthetic time series and validated with a real financial time series: the IBOVESPA stock index (São Paulo Stock Exchange)