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While crop insurance ratemaking has been studied for many decades, it is still faced with many challenges. Crop insurance premium rates (PRs) are traditionally determined only by point estimation, and this approach may lead to uncertainty because it is sensitive to the underwriter’s assumptions regarding the trend, yield distribution, and other issues such as data scarcity and credibility. Thus, the purpose of this paper is to obtain the interval estimate for the PR, which can provide additional information about the accuracy of the point estimate.

A bootstrap method based on the loss cost ratio ratemaking approach is proposed. Using Monte Carlo experiments, the performance of this method is tested against several popular methods. To measure the efficiency of the confidence interval (CI) estimators, the actual coverage probabilities and the average widths of these intervals are calculated.

The proposed method is shown to be as efficient as the non-parametric kernel method, and has the features of flexibility and robustness, and can provide insight for underwriters regarding uncertainty based on the width of the CI.

Comprehensive comparisons are conducted to show the advantage and the efficiency of the proposed method. In addition, a significant empirical example is given to show how to use the CIs to support ratemaking.

The purpose of this paper is to address some of the fundamental issues surrounding crop insurance ratemaking, from the perspective of the reinsurer, through the development of a scientific pricing framework.

The generating process of the historical loss cost ratio's (LCR's) are reviewed, and the Erlang mixture distribution is proposed. A modified credibility approach is developed based on the Erlang mixture distribution and the liability weighted LCR, and information from the observed data of the individual region/province is integrated with the collective experience of the entire crop reinsurance program in Canada.

A comprehensive data set representing the entire crop insurance sector in Canada is used to show that the Erlang mixture distribution captures the tails of the data more accurately compared to conventional distributions. Further, the heterogeneous credibility premium based on the liability weighted LCR's is more conservative, and provides a more scientific approach to enhance the reinsurance pricing.

Credibility models are in the early stages of application in the area of agriculture insurance, therefore, the credibility models presented in this paper could be verified with data from other geographical regions.

The credibility-based Erlang mixture model proposed in this paper should be useful for crop insurers and reinsurers to enhance their ratemaking frameworks.

This is the first paper to introduce the Erlang mixture model in the context of agricultural risk modeling. Two modified versions of the Bühlmann-Straub credibility model are also presented based on the liability weighted LCR to enhance the reinsurance pricing framework.

Federal crop insurance programs are the primary risk management programs of the US farm programs. Currently, these programs have been criticized for being disproportionally in favor of the riskier areas. Despite previous researchers having widely speculated its existence, a formal study of the scale, spatial pattern and fiscal impacts of such misrating phenomenon is still missing in the literature.

This paper first purposes an empirically testable definition of misrating, and then detects the scale of the misrating phenomenon by using over two million actuarial records collected by United States Department of Agriculture (USDA's) risk management agency since 1989. Furthermore, multiple spatial statistics methods have been adopted to study the spatial patterns of the misrating statuses. Finally, the paper builds a simple theoretical model to study the potential fiscal impacts of any policy attempts to mitigate the misrating issue.

The result reveals that roughly 40% of the counties display some degree of misrating. Furthermore, the distribution of misrating displays a significant pattern of positive global spatial autocorrelation, which reflects the existence of regional clusters of premium rate mispricing. Last but not least, the paper concludes that whether an attempt toward fair rating decreases the total program outlay or not relies on the demand elasticity of crop insurance in both overrated and underrated regions.

This paper offers the first attempt to quantify the scale, identify the spatial pattern and evaluate the fiscal impact of the premium misrating in federal crop insurance programs.

The purpose of this paper is to propose an improved reinsurance pricing framework, which includes a crop yield forecasting model that integrates weather variables and crop production information from different geographically correlated regions using a new credibility estimator, and closed form reinsurance pricing formulas. A yield restatement approach to account for changing crop mix through time is also demonstrated.

The new crop yield forecasting model is empirically analyzed based on detailed farm-level data from Manitoba, Canada, covering 216 crop varieties from 19,238 farms from 1996 to 2011. As well, corresponding weather data from 30 stations, including daily temperature and precipitation, are considered. Algorithms that combine screening regression, cross-validation and principal component analysis are evaluated for the purpose of achieving efficient dimension reduction and model selection.

The results show that the new yield forecasting model provides significant improvements over the classical regression model, both in terms of in-sample and out-of-sample forecasting abilities.

The empirical analysis is limited to data from the province of Manitoba, Canada, and other regions may show different results.

This research is useful from a risk management perspective for insurers and reinsurers, and the framework may also be used to develop improved weather risk management strategies to help manage adverse weather events.

This is the first paper to integrate a credibility estimator for crop yield forecasting, and develop a closed form reinsurance pricing formula.

The purpose of this paper is to provide empirical information about the past loss experience in major US crop insurance programs, and documents the impacts of ratings changes through time on the premiums and exposure to participants. The losses are also examined within the structure of the current SRA to identify impacts on insurance companies and the government by fund designation.

- The study uses RMA Summary of Business data and methods consistent with the use of loss-cost ratemaking to analyze loss performance across years with different starting prices and volatilities. Additionally, the RMA premium quoting system was replicated across years with the ability to adjust only one feature at a time to isolate the impacts of changes in individual rating elements from changes in market conditions. Tabulations are provided in map and table form to present the loss ratios through time, in aggregate across time, and within each of the possible funds in which exposures are held. Additionally, the tools developed allow a direct tabulation of the farmer-level premium impacts of individual changes in the policy premium system, and of changing conditions over time.

Corn and soybeans represent dominant shares of aggregate policy premiums and liability, and also are the crops that underwent the greatest degree of revision in rates over the recent past both due to rate study implications, and to loss rate experience. Despite commonly made arguments that payments associated with the drought of 2012 “more than wiped out all historic gains,” it appears that insurance worked very much as intended and that the loss ratios through time are within reasonable ranges of targets. Fund designation, and the separation under the most recent SRA of Group 1 and Group 2 states substantially dampened the loss sharing and ability to capture gains by private companies, and leads to fairly low rates of return on a pure fund-loss sharing basis for insurance companies. Finally, despite the extreme losses of 2012, the aggregate performance of corn relative to the remainder of the program exhibits lower than average loss rates both in aggregate and on a scale-adjusted basis.

The study provides an important means to isolate and assess implications of rate changes, and to associate causes of losses with rate charges. Additionally, the structure of the SRA, and possible future versions of the SRA are informed by both the aggregate, and the normalized performance results provided. And, the relative performance of major row, crops even with recent extreme losses, appears appropriate or positive to insurance companies after considering the impacts of the SRA on company exposure. In total, the evidence points toward appropriate movement toward target overall loss ratios in the US crop insurance program.

This paper provides an extensive empirical evaluation of ratings for major crop insurance policies and provides a unique means to decompose sources of changes in premiums and rates across locations and through time. It also provides an evaluation of the performance of crop insurance post-SRA in a manner that allows both totals and scale-adjusted performance to be assessed.

The purpose of this paper is to review some challenges of insuring weather risk in agriculture and to discuss potential remedies for these problems.

The paper is developed as a narrative on weather insurance based largely on existing literature.

Weather risks show characteristics that often violate classical requirements for insurability. First, some weather risks, particularly slowly emerging weather perils like drought, are spatially correlated and cause systemic risks. Second, climatic change may increase the volatility of weather variables and lead to non-stationary loss distributions, which causes difficulties in actuarial ratemaking. Third, limited availability of yield and weather data hinders the estimation of reliable loss distributions.

Some of the approaches discussed in this review, such as time diversification, local test procedures and the augmentation of observational data by expert knowledge, can be useful for crop insurance companies to improve their risk management and product design.

This study provides background and development information regarding weather insurance and also presents statistical tools and actuarial methods that support the assessment of weather risks as well as the design of weather and yield insurance products.

This paper aimed to study the price of health insurance for individuals aged 65 years and over.

A sample of private health policyholders in Spain is analysed. Joint models are estimated for men and women, separately. A log-linear model of the transformed cumulated number of claims associated with emergency room occupation, ambulance use and hospitalization is estimated, together with a proportional hazard survival model.

The association between the longitudinal process of severe medical care and the survival time process is positive and highly significant for both men and women. An increase in the price of health insurance because of the effect of a larger number of emergency care demand events is slightly offset by the decrease in expected longevity.

The effect of an increase in the number of claims is small compared to the reduction in survival, so age still plays a central role in ratemaking.

High rates of health insurance for elderly insureds should be compensated with younger insureds in the portfolio.

Affordable health insurance premiums for elderly people are difficult to obtain only with strict actuarial principles.

The proposed methodology allows dynamic rates to be designed, so that the price of health insurance can change as new usage information becomes available.

The purpose of this research is to investigate the degree to which trends and structural change may have altered crop insurance expected loss cost ratios across time. Because loss experience is used to set rates for the program, these changes can impact the premiums paid by producers and cost to the government.

County level adjusted loss cost data was merged with climate division weather data for the 1980‐2009 period. Crop‐specific regional‐level regression models were estimated to test for trends and structural changes in the loss experience for major crops (corn, soybeans, sorghum, cotton, winter wheat, and spring wheat). Climate data was used to control for the effect of weather.

For several crops and regions, a significant break point in the loss cost data is found at 1995. This is consistent with the policy changes that occurred in in the program due to the 1994 legislative change. In most instances loss experience prior to 1995 is higher than more recent years even when controlling for the effect of weather. The exception is in winter wheat where it appears recent experience may be worse rather than older experience.

This paper provides a large‐scale assessment of the magnitude of improved crop insurance loss experience across time.

Antitrust exemptions to shipping alliances in the liner shipping sector have prevailed for many years. This study aims to examine anti-competition of ocean shipping alliances from a legal perspective of the USA, the European Union (EU) and People’s Republic of China (PRC).

Adopting the standard “doctrinal approach to legal research and analysis” in legal literatures, this paper reviews landmark court cases and legislations in the USA relating to shipping conference system from its beginning to its erosion, followed by its latest transition to non-ratemaking agreements, with discussions on the EU and some PRC treatments on shipping conferences.

Although antitrust exemptions to shipping conferences in the liner shipping sector were eliminated in the trades to/from the USA and the EU, there is a lack of evidence of the deterioration found in the viability of liner shipping carriers in both parts of the world trades. For the USA, shipping alliances will shift the focus to sharing resources for improvement of collective operational efficiencies, whereas the shipper groups in the EU have worried that a protected system of sharing information may lead to price fixing conducts among the carriers.

Through the discussions on the legal treatments of shipping conferences from the USA, the EU and PRC perspectives, this paper provides legal researchers with not only a new research direction on raising collective operational efficiencies through resource sharing but also an insight into shifting their research focus from purely price determination to the area of merger.

This paper reviews landmark court cases and related legislations about the treatments of different regulatory regimes, including the USA, the EU and PRC, to explore the illegitimacy of anti-competition conducts in ocean shipping alliances.

Type of article Theoretical with worked example