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.     

Comparisons of Bayesian estimation procedures for two-way contingency tables without interaction

Bayesian and empirical Bayesian estimation methods are reviewed and proposed for the row and column parameters in two-way Contingency tables without interaction. Rasch's multiplicative Poisson model for misreadings is discussed in an example. The case is treated where assumptions of exchangeability are reasonable a priori for the unknown parameters. Two different types of prior distributions are compared, It appears that gamma priors yield more tractable results than lognormal priors.     

聚合信用风险模型的改进和研究

近年来的研究发现,违约损失率的分布呈现一种双峰特征。文章对传统聚合信用风险模型进行改进,用具有双峰特征的双beta分布来刻画违约损失率的变化,给出全部贷款组合信用风险概率生成函数的解析式,利用数值模拟的结果验证了模型的有效性。     

Finding Pareto Optimal Insurance Contracts

This paper deals with on-line computation—or step-wise learning—of Pareto optimal insurance contracts. Our approach tolerates that the loss distribution might be unknown, intractable, or not well specified. Thus we accommodate fairly inexperienced parties. Losses are here simulated or observed, one at a time, and they cause iterated revisions of the premium. The mechanical and global nature of probability calculus thereby yields to more tentative, myopic procedures, possibly closer to how humans operate or reason in face of risk. Sequential revisions may also reduce the expense of insurers' time and money in seeking sufficient statistics. Emphasized below is the remarkable simplicity and stability of the resulting adaptive procedures. Special attention goes to catastrophic risks, and to subsidized or competitive insurance.     

A new higher-order weak approximation scheme for stochastic differential equations and the Runge–Kutta method

The authors report on the construction of a new algorithm for the weak approximation of stochastic differential equations. In this algorithm, an ODE-valued random variable whose average approximates the solution of the given stochastic differential equation is constructed by using the notion of free Lie algebras. It is proved that the classical Runge–Kutta method for ODEs is directly applicable to the ODE drawn from the random variable. In a numerical experiment, this is applied to the problem of pricing Asian options under the Heston stochastic volatility model. Compared with some other methods, this algorithm is significantly faster. This research was partly supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), 15540110, 2003 and 18540113, 2006, the 21st century COE program at Graduate School of Mathematical Sciences, the University of Tokyo, and JSPS Core-to-Core Program 18005.     

Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis

We empirically compare Libor and Swap Market Models for thepricing of interest rate derivatives, using panel data on pricesof US caplets and swaptions. A Libor Market Model can directlybe calibrated to observed prices of caplets, whereas a SwapMarket Model is calibrated to a certain set of swaption prices.For both models we analyze how well they price caplets and swaptionsthat were not used for calibration. We show that the Libor MarketModel in general leads to better prediction of derivative pricesthat were not used for calibration than the Swap Market Model.Also, we find that Market Models with a declining volatilityfunction give much better pricing results than a specificationwith a constant volatility function. Finally, we find that modelsthat arechosen to exactly match certain derivative prices areoverfitted; more parsimonious models lead to better predictionsfor derivative prices that were not used for calibration. JELClassification: G12, G13, E43.     

On a stochastic approximation procedure based on averaging

Based on the idea of averaging a new stochastic approximation algorithm has been proposed by Bather (1989), which shows a preferable performance for small to moderate sample sizes. In the present paper an almost sure representation is established for this procedure, which gives the optimal rate of convergence with minimal asymptotic variance. Work partly supported by the research grant Ku719/2-1 of the Deutsche Forschungsgemeinschaft