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.     

Smoothing the payoff for efficient computation of Basket option prices

We consider the problem of pricing basket options in a multivariate Black–Scholes or Variance-Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high-dimensional numerical integration problems with non-smooth integrands. Due to this lack of regularity, higher order numerical integration techniques may not be directly available, requiring the use of methods like Monte Carlo specifically designed to work for non-regular problems. We propose to use the inherent smoothing property of the density of the underlying in the above models to mollify the payoff function by means of an exact conditional expectation. The resulting conditional expectation is unbiased and yields a smooth integrand, which is amenable to the efficient use of adaptive sparse-grid cubature. Numerical examples indicate that the high-order method may perform orders of magnitude faster than Monte Carlo or Quasi Monte Carlo methods in dimensions up to 35.     

Turning from crime: A dynamic perspective

This paper examines criminal choice using a variant of the human capital model. The innovation of our approach is that it attempts to disaggregate individual capital, not unlike production-based studies which disaggregate physical capital into equipment and structures. We disaggregate an individual’s capital stock into the standard human capital component as well as a utility generating component that we call social capital. In our set-up, social capital is used to account for the influence of social norms on the decision to participate in crime. This is done by modeling the stigma of arrest as a reduction in the individual’s social capital stock. We also allow individuals to account for the impact of their criminal actions on their probability of arrest. In order to estimate the structural parameters underlying the model, we make use of computationally intensive methods involving simulated generalized method of moments and value function approximation. The empirical results, based on panel data from the Delinquency in a Birth Cohort II Study, support the social capital model of crime and reveal significant state dependence in the decision to participate in crime.     

Impact evaluation for tourism development using the fuzzy set model: A case study of Kyongju,Korea

The Community tourism industry is primarily influenced by facilities, traffic systems, capacity, and development of tourism commodities. To develop tourism industry on a local basis, it is unavoidable to make investments on a large scale. Factor analysis for impact evaluation prior to undertaking of development projects, which this study intends to make, is more reasonable when related to the fuzzy numeric analysis of words or sentences than to a quantitative analysis of measured information. In this study the Euclidean distance method and Zadeh's fuzzy extension principle were used as linguistic approximation to establish the validity of decision‐ making in each factor category of impact degree. Therefore, this study introduces a general concept of Fuzzy theory through literature review of linguistic expressions. This study examined availability of the Fuzzy model in analyzing investment priorities for tourist development and applied it to Kyongju area, which unveiled the priorities for Kyongju tourism future in order of traffic system improvement, early construction of horse‐ racing track now under planning, promotion of Kyongju as tourism special zone to visitors and positive tourism events. In terms of methodology, this study disclosed that Fuzzy Model approach is greatly useful to decision‐making processes in tourist development.     

Multi‐state Stochastic Processes: A Statistical Flowgraph Perspective

Two‐state models (working/failed or alive/dead) are widely used in reliability and survival analysis. In contrast, multi‐state stochastic processes provide a richer framework for modeling and analyzing the progression of a process from an initial to a terminal state, allowing incorporation of more details of the process mechanism. We review multi‐state models, focusing on time‐homogeneous semi‐Markov processes (SMPs), and then describe the statistical flowgraph framework, which comprises analysis methods and algorithms for computing quantities of interest such as the distribution of first passage times to a terminal state. These algorithms algebraically combine integral transforms of the waiting time distributions in each state and invert them to get the required results. The estimated transforms may be based on parametric distributions or on empirical distributions of sample transition data, which may be censored. The methods are illustrated with several applications.     

On the performance of the ordinary least squares method under an error component model

Starting from the one-dimensional results by Wang et al (1994) we consider the performance of the ordinary least squares estimator in comparison to the best linear unbiased estimator under an error component model with random effects in units and time. Upper bounds are derived for the first-order approximation to the difference between both estimators and for the spectral norm of the difference between their dispersion matrices.     

Valuation and applications of compound basket options

This study investigates compound basket options, which are options on portfolios of options. Although they may be new to financial markets, they are available as equity basket options, equity spread options, stocks of holding companies, and collateralized debt obligations. Using moments of portfolio values, we provide formulas for pricing compound basket options. According to numerical analysis, a lower bound and a weighted average of bounds yield relatively small errors. Additionally, ignoring the compound feature increases the pricing error of equity basket options because the feature captures the capital structure and leverage effect of stock prices.     

Exact likelihood computation for nonlinear DSGE models with heteroskedastic innovations

Phenomena such as the Great Moderation have increased the attention of macroeconomists towards models where shock processes are not (log-)normal. This paper studies a class of discrete-time rational expectations models where the variance of exogenous innovations is subject to stochastic regime shifts. We first show that, up to a second-order approximation using perturbation methods, regime switching in the variances has an impact only on the intercept coefficients of the decision rules. We then demonstrate how to derive the exact model likelihood for the second-order approximation of the solution when there are as many shocks as observable variables. We illustrate the applicability of the proposed solution and estimation methods in the case of a small DSGE model.     

Chi-Square Tests Under Models Close to the Normal Distribution

Many test statistics follow a χ² distribution because a normal model is assumed as underlying distribution. In this paper we obtain good analytic approximations for the p-value and the critical value of χ² tests when the underlying distribution is close but different from the normal model. With these approximations we study the robustness of validity of χ² tests     

Convergence of stochastic approximation algorithms under irregular conditions

We consider a class of stochastic approximation (SA) algorithms for solving a system of estimating equations. The standard condition for the convergence of the SA algorithms is that the estimating functions are locally Lipschitz continuous. Here, we show that this condition can be relaxed to the extent that the estimating functions are bounded and continuous almost everywhere. As a consequence, the use of the SA algorithm can be extended to some problems with irregular estimating functions. Our theoretical results are illustrated by solving an estimation problem for exponential power mixture models.