A stochastic model to evaluate pricing distortions in indemnity insurance methods for MTPL insurance

Direct compensation or the direct reimbursement scheme is an indemnity insurance method that many European and American countries use to manage motor liability claims in which the driver that suffers an accident is paid by his/her insurance company that possibly later receives a flat-rate reimbursement (known as forfeit). Using non-life actuarial methodologies, this article analyses the distortion effects due to the direct compensation mechanisms and the effects of different forfeit reimbursement systems on policyholder tariffs in the management of motor liability claims involving vehicles in two different sectors, i.e. automobile and motorcycle. We empirically analyse and formalize the distortion effects resulting from the mechanism that different direct reimbursement systems produce, and explore the correlation between increasing tariffs for motorcycle policyholders and decreasing tariffs for other vehicle policyholders. We propose some alternative methods to overcome these distortion effects, evaluating their pricing impact through a stochastic model applied to a case study.

     

Public transit bus procurement: The role of energy prices,regulation and federal subsidies

The U.S. public transit system represents a multi-billion dollar industry that provides essential transit services to millions of urban residents. We study the market for new transit buses that features a set of non-profit transit agencies purchasing buses primarily from a few domestic bus makers. In contrast with private passenger vehicles, the fuel economy of public buses has not improved during the last thirty years and is irresponsive to fuel price changes. To understand these findings, we build a model of bus fleet management decisions of public transit agencies that yields testable hypotheses. Our empirical analysis of bus fleet turnover and capital investment highlights the role of energy prices, environmental regulations, and the “Buy America” mandate associated with receiving federal funding to purchase public transit buses.     

Forecasting automobile insurance paid claim costs using econometric and ARIMA models

Automobile insurance companies in the United States currently utilize simple exponential trend models to forecast paid claim costs, an important variable in ratemaking. This paper tests the performance of econometric and ARIMA models, as well as the current insurance industry method, in forecasting two paid claim cost series. The experiments encompass eight forecast periods ranging from 1974 through early 1983. The results indicate that automobile insurers could significantly improve their forecasts of property damage liability claim costs by adopting econometric models. For bodily injury liability claim costs, the accuracy of the econometric and insurance industry methods is approximately the same, and both outperform the ARIMA models. Overall, a net gain in accuracy could be achieved by adopting econometric models.     

贝叶斯非线性分层模型在多元索赔准备金评估中的应用

本文将贝叶斯非线性分层模型应用于基于不同业务线的多元索赔准备金评估中,设计了一种合适的模型结构,将非线性分层模型与贝叶斯方法结合起来,应用WinBUGS软件对精算实务中经典流量三角形数据进行建模分析,并使用MCMC方法得到了索赔准备金完整的预测分布。这种方法扩展并超越了已有多元评估方法中最佳估计和预测均方误差估计的研究范畴。在贝叶斯框架下结合后验分布实施推断对非寿险公司偿付能力监管和行业决策具有重要作用。     

Bayesian inference in a sample selection model

This paper develops methods of Bayesian inference in a sample selection model. The main feature of this model is that the outcome variable is only partially observed. We first present a Gibbs sampling algorithm for a model in which the selection and outcome errors are normally distributed. The algorithm is then extended to analyze models that are characterized by nonnormality. Specifically, we use a Dirichlet process prior and model the distribution of the unobservables as a mixture of normal distributions with a random number of components. The posterior distribution in this model can simultaneously detect the presence of selection effects and departures from normality. Our methods are illustrated using some simulated data and an abstract from the RAND health insurance experiment.     

A bidimensional approach to mortality risk

Abstract We analyze the evolution over time of portfolios of life insurance contracts referring to different cohorts or risk classes of insureds. We model the intensity of mortality as a random field, in order to capture cross-generation (risk class) effects induced by the on-going management of portfolios of policies. Applications are described in the context of mortality risk analysis and (market) valuation of liabilities at aggregate level. It is shown how the model can be employed when an insurer’s new business is considered.     

Estimating willingness to pay for medicare using a dynamic life-cycle model of demand for health insurance

Medicare is the largest health insurance program in the US. This paper uses a dynamic random utility model of demand for health insurance in a life-cycle human capital framework with endogenous production of health to calculate the individual willingness to pay (WTP) for Medicare. The model accounts for the feature that the demand for health insurance is derived through the demand for health, which is jointly determined with the production of health over the life-cycle. The WTP measure incorporates the effects of Medicare insurance on aggregate consumption through effects on medical expenditures and mortality, and consumption utility of health. The model is estimated using panel data from the Health and Retirement Study. The average WTP or change in lifetime expected utility resulting from delaying the age of eligibility to 67 is found to be $ 24,947 in 1991 dollars ($ 39,435 in 2008 dollars). However, there is considerable variation in the WTP, e.g., in 1991 dollars the WTP of individuals who have less than a high school education and are white is $ 28,347 ($ 44,810 in 2008 dollars), while the WTP of those with at least a college degree and who are neither white nor black is $ 15,584 ($ 24,635 in 2008 dollars). More generally, the less educated have a higher WTP to avoid a policy change that delays availability of Medicare benefits. Additional model simulations imply that the primary benefits of Medicare are insurance against medical expenditures with relatively smaller benefits in terms of improved health status and longevity. Medicare also leads to large increases in medical utilization due to deferring of medical care prior to eligibility.     

Interaction of maritime shipping and hinterland traffic using a two-level hierarchical transport network

A transport scenario based on a two-level network is developed in order to model operations in maritime transport. To enhance competitiveness and sustainability of shipping companies, the interaction between maritime shipping and hinterland traffic is considered in the novel two-level hierarchical transport network. Demand occurs on the second level, the hinterland, whereas the first level, the sea transport, acts as a pure distribution network. The two-level hierarchical transport model allows regulating the degree of interaction a liner operator has regarding the hinterland traffic. Moreover, access of vehicles to nodes or edges is given subject to feasibility constraints, relating to the size of a vehicle. In this work, the relation to existing routing models, such as the travelling salesman problem, the vehicle routing problem, or the travelling purchaser problem, is illustrated. Moreover, through the definition of a proper set of assumptions, it is possible to reduce the considered two-level hierarchical transport network to different standard routing models. These new insights allow the application of existing solution methods. Numerical experiments are conducted for a particular case and illustrate the influence of node costs on the distribution of workload to the vehicles.     

An EM algorithm for the estimation of parametric and nonparametric hierarchical nonlinear models

It is shown how to implement an EM algorithm for maximum likelihood estimation of hierarchical nonlinear models for data sets consisting of more than two levels of nesting. This upward–downward algorithm makes use of the conditional independence assumptions implied by the hierarchical model. It cannot only be used for the estimation of models with a parametric specification of the random effects, but also to extend the two-level nonparametric approach – sometimes referred to as latent class regression – to three or more levels. The proposed approach is illustrated with an empirical application.     

Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects

Gauss–Hermite quadrature is often used to evaluate and maximize the likelihood for random component probit models. Unfortunately, the estimates are biased for large cluster sizes and/or intraclass correlations. We show that adaptive quadrature largely overcomes these problems. We then extend the adaptive quadrature approach to general random coefficient models with limited and discrete dependent variables. The models can include several nested random effects (intercepts and coefficients) representing unobserved heterogeneity at different levels of a hierarchical dataset. The required multivariate integrals are evaluated efficiently using spherical quadrature rules. Simulations show that adaptive quadrature performs well in a wide range of situations.     

Household search and health insurance coverage

Health insurance in the United States is typically acquired through an employer-sponsored program. Often employees offered employer-provided health insurance have the option to extend coverage to their spouse and dependents. We investigate the implications of the “publicness” of health insurance coverage for the labor market careers of spouses. The theoretical innovations in the paper are to extend the standard partial–partial equilibrium labor market search model to a multiple searcher setting with the inclusion of multi-attribute job offers, with some of the attributes treated as public goods within the household. The model is estimated using data from the Survey of Income and Program Participation (SIPP) using a Method of Simulated Moments (MSM) estimator. We demonstrate how previous estimates of the marginal willingness to pay (MWP) for health insurance based on cross-sectional linear regression estimators may be seriously biased due to the presence of dynamic selection effects and misspecification of the decision-making unit.     

Analysis of binary data with the possibility of wrong ascertainment

Most genetic studies recruit high‐risk families, and the discoveries are based on non‐random selected groups. We must consider the consequences of this ascertainment process to apply the results of genetic research to the general population. In addition, in epidemiological studies, binary responses are often misclassified. We proposed a binary logistic regression model that provides a novel and flexible way to correct for misclassification in binary responses, taking into account the ascertainment issues. A hierarchical Bayesian analysis using Markov chain Monte Carlo method has been carried out to investigate the effect of covariates on disease status. The focus of this paper is to study the effect of classification errors and non‐random ascertainment on the estimates of the model parameters. An extensive simulation study indicated that the proposed model results in substantial improvement of the estimates. Two data sets have been revisited to illustrate the methodology.     

Optimal reinsurance with multiple tranches

Motivated by common practices in the reinsurance industry and in insurance markets such as Lloyd’s, we study the general problem of optimal insurance contracts design in the presence of multiple insurance providers. We show that the optimal risk allocation rule is characterized by a hierarchical structure of risk sharing where all agents take on risks only above the endogenously determined thresholds, or agent-specific deductibles. Linear risk sharing between two adjacent thresholds is shown to be optimal when all agents have CARA utilities. Furthermore, we show that the optimal thresholds can be efficiently calculated through the fixed point of a contraction mapping.     

Hierarchical models for independence structures of networks

We introduce a new family of network models, called hierarchical network models, that allow us to represent in an explicit manner the stochastic dependence among the dyads (random ties) of the network. In particular, each member of this family can be associated with a graphical model defining conditional independence clauses among the dyads of the network, called the dependency graph. Every network model with dyadic independence assumption can be generalized to construct members of this new family. Using this new framework, we generalize the Erdös–Rényi and the β models to create hierarchical Erdös–Rényi and β models. We describe various methods for parameter estimation, as well as simulation studies for models with sparse dependency graphs.     

Is econometrics useful for private policy making? A case study of replacement policy at an auto rental company

The goal of this paper is to illustrate the potential usefulness of econometrics as a tool to assist private policy makers. We provide a case study and detailed econometric analysis of the automobile replacement policy adopted by a large car rental company. Unlike public policy making–where the benefits from using econometric models and “science-based” approaches to policy making are hard to quantify because the outcomes of interest are typically subjective quantities such as “social welfare”–in the case of firms there is an objective, easily quantifiable criterion for judging whether policy A is better than policy B: profits. We introduce and estimate an econometric model of the rental histories of individual cars in the company’s fleet. Via stochastic simulations, we show that the model provides a good approximation to the company’s actual operations. In particular, the econometric model is able to reproduce the extraordinarily high rates of return that the company obtains on its rental cars, with average internal rates of return between purchase and sale of approximately 50%. However, the econometric model can simulate outcomes under a range of counterfactual vehicle replacement policies. We use the econometric model to simulate the profitability of an alternative replacement policy under pessimistic assumptions about the rate maintenance costs would increase and rental rates would have to be decreased if the company were to keep its rental cars longer than it does under the status quo. Depending on the vehicle type, we find that the company’s expected discounted profits would be between 6% to over 140% higher under the suggested alternative operating strategy where vehicles are kept longer and rental rates of older vehicles are discounted to induce customers to rent them. The company found this analysis to be sufficiently convincing that it undertook an experiment to verify the predictions of the econometric model.     

Scheduling food bank collections and deliveries to ensure food safety and improve access

Food banks are privately-owned non-profit organizations responsible for the receipt, processing, storage, and distribution of food items to charitable agencies. These charitable agencies in turn distribute food to individuals at risk of hunger. Food banks receive donated food from national and local sources, such as The Emergency Food Assistance Program (TEFAP) and supermarkets. Local sources with frequent high-volume donations justify the use of food bank vehicles for collection. Food bank vehicles are also used to deliver food to rural charitable agencies that are located beyond a distance safe for perishable food to travel without spoilage. Due to limited funds, food banks can only afford to sparingly use their capital on non-food items. This requires exploring more cost effective food delivery and collection strategies. The goal of this paper is to develop transportation schedules that enable the food bank to both (i) collect food donations from local sources and (ii) to deliver food to charitable agencies. We identify satellite locations, called food delivery points (FDPs), where agencies can receive food deliveries. A set covering model is developed to determine the assignment of agencies to an FDP. Both vehicle capacity and food spoilage constraints are considered during assignment. Using the optimal assignment of agencies to FDPs, we identify a weekly transportation schedule that addresses collection and distribution of donated food and incorporates constraints related to food safety, operator workday, collection frequency, and fleet capacity.     

Correlated income shocks and excess smoothness of consumption

In the literature, econometricians typically assume that household income is the sum of a random walk permanent component and a transitory component, with uncorrelated permanent and transitory shocks. Using data on realized individual incomes and individual expectations of future incomes from the Survey of Italian Households׳ Income and Wealth, I find that permanent and transitory shocks are negatively correlated. Relaxing the assumption of no correlation between the shocks, I explore the effects of correlated income shocks on the estimated consumption insurance against permanent and transitory shocks, and consumption smoothness using a life-cycle model with self-insurance calibrated to U.S. data. Negatively correlated income shocks result in smoother consumption, and upward-biased estimates of the insurance against transitory (and permanent when borrowing constraints are not tight) income shocks. While the life-cycle model with negatively correlated shocks fits well the sensitivity of consumption to current income shocks observed in U.S. data, it falls short of explaining the sensitivity of consumption to income shocks cumulated over a longer horizon.     

Health insurance and retirement of married couples

Most health insurance in the USA is provided by employers until eligibility for public health insurance (Medicare) begins at age 65. Retiring before 65 exposes workers who lack retiree health insurance coverage to the risk of catastrophic medical expenditure. We solve and estimate a dynamic model of the employment behavior of older married couples that includes risky medical expenditure and health insurance. Parameter estimates imply that the risk‐reducing feature of health insurance can account for about half of the observed association between retiree health insurance and employment for married men, but can account for only one tenth of the much larger observed association for married women. Policy simulations imply very small effects on employment of changing the age of eligibility for Medicare from 65 to 67. Copyright © 2006 John Wiley & Sons, Ltd.     

Estimating heterogeneous capacity and capacity utilization in a multi-species fishery

We use a stochastic production frontier model to investigate the presence of heterogeneous production and its impact on fleet capacity and capacity utilization in a multi-species fishery. We propose a new fleet capacity estimate that incorporates complete information on the stochastic differences between vessel-specific technical efficiency distributions. Results indicate that ignoring heterogeneity in production technologies within a multi-species fishery as well as the complete distribution of a vessel’s technical efficiency score, may lead to erroneous fleet-wide production profiles and estimates of capacity. Our new estimate of capacity enables out-of-sample production predictions which may be useful to policy makers.     

养老保险统筹层次收入再分配系数及全国统筹类型研究

本文从社会统筹养老保险的收入再分配功能入手,根据养老金计发办法及约束因素,提出“基础养老金收入再分配系数”原理和数理模型,据此延伸出分层平均统筹类型与分比例统筹类型下全国统筹各方案,测算全国统筹各方案下的收入再分配系数并依据希克斯改进、生存公平、劳动公平三种检验,评估全国统筹各方案的收入再分配效果。研究表明：选择方案5（10%替代率中央统筹分比例统筹类型）作为养老保险全国统筹起步方案,实现了适度的收入再分配,可以稳妥地衔接地区之间的利益关系,实现省级统筹向全国统筹的合理对接。