Spatial statistical modelling of insurance risk: a spatial epidemiological approach to car insurance

Spatial models, such as the Besag, York and Mollie (BYM) model, have long been used in epidemiology and disease mapping. A common research question in these subjects is modelling the number of disease events per region; here the BYM models provides a holistic framework for both covariates and dependencies between regions. We use these tools to assess the relative insurance risk associated with the policyholders geographical location. A Bayesian modelling approach is presented and an elastic net is used to reduce the large number of possible geographic covariates. The final inference is performed using Integrated Nested Laplace Approximation. The model is applied to car insurance data from If P&C Insurance together with spatially referenced covariate data of high resolution, provided by Insightone. The entire analysis is performed using freely available R-packages. Including spatial dependence when modelling the number of claims significantly improves on the result obtained using ordinary generalised linear models. However, the support for adding a spatial component to the model for claims cost is weaker.     

电网故障模型中贝叶斯网络和DS证据理论的应用

由于电网的复杂性和多变性,导致电网故障中存在信息不确定性问题,这就需要依靠贝叶斯网络和DS证据理论的自动生成方法。文章主要描述了这两种方法的原理,讨论了贝叶斯网络和DS证据理论在电网故障模型领域应用的可能方式和情况,并运用一些实例证明了这种方法的可靠性。     

Bayesian semiparametric stochastic volatility modeling

This paper extends the existing fully parametric Bayesian literature on stochastic volatility to allow for more general return distributions. Instead of specifying a particular distribution for the return innovation, nonparametric Bayesian methods are used to flexibly model the skewness and kurtosis of the distribution while the dynamics of volatility continue to be modeled with a parametric structure. Our semiparametric Bayesian approach provides a full characterization of parametric and distributional uncertainty. A Markov chain Monte Carlo sampling approach to estimation is presented with theoretical and computational issues for simulation from the posterior predictive distributions. An empirical example compares the new model to standard parametric stochastic volatility models.     

Bayesian–Walrasian equilibria: beyond the rational expectations equilibrium

In general rational expectations equilibrium (REE), as introduced in Radner (Econometrica 47:655–678, 1978) in an Arrow–Debreu–McKenzie setting with uncertainty, does not exist. Moreover, it fails to be fully Pareto optimal and incentive compatible and is also not implementable as a perfect Bayesian equilibrium of an extensive form game (Glycopantis et al. in Econ Theory 26:765–791, 2005). The lack of all the above properties is mainly due to the fact that the agents are supposed to predict the equilibrium market clearing price (as agent’s expected maximized utility is conditioned on the information that equilibrium prices reveal), which leads inevitably to the presumption that agents know all the primitives in the economy, i.e., random initial endowments, random utility functions and private information sets. To get around this problematic equilibrium notion, we introduce a new concept called Bayesian–Walrasian equilibrium (BWE) which has Bayesian features. In particular, agents try to predict the market-clearing prices using Bayesian updating and evaluate their consumption in terms of Bayesian price estimates, which are different for each individual. In this framework agents maximize expected utility conditioned on their own private information about the state of nature, subject to a Bayesian estimated budget constraint. Market clearing is not an intrinsic part of the definition of BWE. However, both in the case of perfect foresight and in the case of symmetric information BWE leads to a statewise market clearing; it then becomes an ex post Walrasian equilibrium allocation. This new BWE exists under standard assumptions, in contrast to the REE. In particular, we show that our new BWE exists in the well-known example in Kreps (J Econ Theory 14:32–43, 1977), where REE fails to exist. This work was done in the Spring of 2005, when EJB was a visiting professor at the University of Illinois.