Lysa Porth

A credibility-based Erlang mixture model for pricing crop reinsurance

Purpose - – 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. Design/methodology/approach - – The generating process of the historical loss cost ratios (LCRs) 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. Findings - – 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 LCRs is more conservative, and provides a more scientific approach to enhance the reinsurance pricing. Research limitations/implications - – 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. Practical implications - – The credibility-based Erlang mixture model proposed in this paper should be useful for crop insurers and reinsurers to enhance their ratemaking frameworks. Originality/value - – This is the first paper to introduce the Erlang mixture model in the context of agricultural risk modeling. Two modified versions of the Buhlmann-Straub credibility model are also presented based on the liability weighted LCR to enhance the reinsurance pricing framework.

Insurance Premium Calculation Using Credibility Analysis: An Example from Livestock Mortality Insurance

A major problem facing livestock producers is animal mortality risk. Livestock mortality insurance is still at the initial stages, and premium computation approaches are still relatively new and will require more research. This study seeks to provide a first step for developing a better understanding of livestock insurance as a solution to mortality risk, as it explores improved methods for livestock mortality insurance modeling procedures, and premium computation, using credibility analysis. The purpose of this study is to develop improved estimates for livestock mortality insurance premiums for Canada under a credibility framework. We illustrate our approach through one example using livestock data from 1999 to 2007.

A bootstrap approach for pricing crop yield insurance

Purpose - 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. Design/methodology/approach - 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. Findings - 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. Originality/value - 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.

Factors affecting farmers’ willingness to purchase weather index insurance in the Hainan Province of China

Purpose - – The purpose of this paper is to explain the factors affecting farmers’ willingness to purchase weather index insurance for crops in China, in the Province of Hainan, and to also provide additional background information on weather index insurance. Design/methodology/approach - – A survey of 134 farmers was undertaken in Hainan, China, regarding their willingness to purchase weather index insurance. A probit regression model was used, and a number of variables were included to explain willingness of farmers to purchase weather index insurance. Findings - – In total, 11 of 15 variables in the model are found to be statistically significant in explaining farmers’ willingness to purchase weather index insurance. Research limitations/implications - – First, farmers’ interest in weather index insurance may be limited due to basis risk. Second, some farmers may not sufficiently understand weather index insurance and so may not purchase it, and a considerable portion of farmers may also require a subsidy if they are to purchase weather insurance. Practical implications - – Weather index insurance may provide a lower cost alternative than traditional crop insurance, however, basis risk remains a main challenge. Originality/value - – This is the first study to quantitatively study the factors affecting the willingness of farmers to purchase weather index insurance for agriculture in the province of Hainan, China.

A Credibility-Based Yield Forecasting Model for Crop Reinsurance Pricing and Weather Risk Management

Purpose - 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. Design/methodology/approach - 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. Findings - 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. Research limitations/implications - The empirical analysis is limited to data from the province of Manitoba, Canada, and other regions may show different results. Practical implications - 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. Originality/value - This is the first paper to integrate a credibility estimator for crop yield forecasting, and develop a closed form reinsurance pricing formula.

On a Class of Premium Calculation Principles Based on the Multivariate Weighted Distribution

This paper proposes a new class of premium calculation principles based on the multivariate weighted distribution, where risk loadings are imposed by transforming the density of the underlying actuarial risk by encompassing a number of external risk factors. This is a highly flexible class of premium principle with a number of desirable characteristics, including scale and translation invariance, additivity, stochastic dominance preserving, and additivity for layers. It is also shown that by appropriately selecting external risk factors, this premium principle has increasing relative risk loading. This is important for pricing layered insurance contracts, which is common for many property and casualty insurance programs, such as for agriculture, hurricanes, etc. This premium principle is important for actuarial pricing practice in the sense that it is able to integrate additional important information into the pricing framework, such as market conditions, economic conditions, catastrophic events, etc. Two pricing examples are presented to demonstrate the statistical advantages and empirical application of the new premium principle proposed in this paper.

A Relational Model for Predicting Farm-Level Crop Yield Distributions in the Absence of Farm-Level Data

The focus of this article is on predictive analytics regarding data scarcity and credibility, which are major difficulties facing the agricultural insurance sector, often due to limited loss experi...

Spatial Dependence & Aggregation in Weather Risk Hedging

Adverse weather related risk is a main source of crop production loss, and in addition to farmers, this exposure is a major concern and uncertainty for insurers and reinsurers who act as weather risk underwriters. To date, weather hedging has had limited success, largely due to challenges regarding basis risk. Therefore, this paper develops and compares different weather risk hedging strategies for agricultural insurers and reinsurers, through investigating the spatial dependence and aggregation level of systemic weather risks across a country. This paper proposes a flexible time series model that assumes a general hyperbolic (GH) family for the margins to capture the heavy-tail property of the data, together with the Levy subordinated hierarchical Archimedean copula (LSHAC) model to overcome the challenge of high-dimensionality in modeling the dependence of weather risk. Wavelet analysis is employed to study the detailed characteristics within the data from both time and frequency scales. The analysis shows that the LSHAC model proposed in this paper reduces extreme weather downside risk by

Livestock mortality insurance: development and challenges

3920.89 million, providing an additional

Optimal Reinsurance Analysis from a Crop Insurer's Perspective

321.61 million risk reduction compared to the independent model assumption. Further, the results reveal that more effective hedging may be achieved as the spatial aggregation level increases.