Tippatai Pongsart

Insurance serves as a mechanism to effectively manage and transfer revenue-related risks. We conducted a study to explore the potential financial advantages of index insurance, which protects agricultural producers, specifically sugarcane, against excessive rainfall. Creation of the index involved utilizing generalized additive regression models, allowing for consideration of non-linear effects and handling complex data by adjusting the complexity of the model through the addition or reduction of terms. Moreover, quantile generalized additive regression was deliberated to evaluate relationships with lower quantiles, such as low-yield events. To quantify the financial benefits for farmers, should they opt for excessive rainfall index insurance, we employed efficiency analysis based on metrics such as conditional tail expectation (CTE), certainty equivalence of revenue (CER), and mean root square loss (MRSL). The results of the regression model demonstrate its accuracy in predicting sugar cane yields, with a split testing R² of 0.691. MRSL should be taken into consideration initially, as it is a farmer’s revenue assessment that distinguishes between those with and those without insurance. As a result, the GAM model indicates the least fluctuation in farmer income at the 90th percentile. Additionally, our study suggests that this type of insurance could apply to sugarcane farmers and other crop producers in regions where extreme rainfall threatens the financial sustainability of agricultural production.

Insurance serves as a mechanism to effectively manage and transfer revenue-related risks. We conducted a study to explore the potential financial advantages of index insurance, which protects agricultural producers, specifically sugarcane, against excessive rainfall. Creation of the index involved utilizing generalized additive regression models, allowing for consideration of non-linear effects and quantile generalized additive regression to evaluate relationships with lower quantiles, such as low yield events. To quantify the financial benefits for farmers, should they opt for excessive rainfall index insurance, we employed efficiency analysis based on metrics such as Conditional Tail Expectation, Certainty Equivalence of Revenue, and Mean Root Square Loss. The results of the regression model demonstrate its accuracy in predicting sugar cane yields, with a split testing R2 of 0.691. Additionally, our study suggests that this type of insurance could also apply to sugarcane farmers and other crop producers in regions where extreme rainfall threatens the financial sustainability of agricultural production.

The bonus-malus system (BMS) is one of the most widely used tools in merit-rating automobile insurance, with the primary goal of ensuring that fair premiums are paid by all policyholders. The traditional BMS is dependent only on the claim frequency. Thus, an insured person who makes a claim with a small severity is penalized unfairly compared to an individual who makes a large severity claim. This study proposes a model for estimating the bonus-malus premium by employing a limit value (monetary unit) which distinguishes claim size into small and large based on claim frequency and claim severity distributions. This assists in determining the penalties for policyholders with claim sizes falling above and below the limit value. The number of claims is assumed to follow a Poisson distribution, and the total number of claims with a size greater than the limit value is considered a binomial distribution. The underlying risk of each policyholder is assumed to follow a beta Lindley distribution and is referred to as the prior distribution. Each policyholder’s claim size is also assumed to follow a gamma distribution, with the Lindley distribution considered as the prior distribution. Bonus-malus premiums are calculated following the Bayesian method. Practical examples using an actual data set are provided, and the results generated are compared to those produced using the traditional Poisson binomial-exponential beta model. This methodology provides a more equitable mechanism for penalizing policyholders in the portfolio.

The premium calculation considered in the classical bonus-malus system in automobile insurances is dependent only on a number of claims. When a policyholder declared a small claim size, he or she was penalized in the same way as those who made a large claim size. Hence, it is unfair to penalize all policyholders in like manner. In this article, we propose a model for computing the premium based on the bonus-malus system by distinguishing multiple types of claims as follows: small, middle, large, and sever claim sizes. The number of claims is considered based on discrete distributions: Poisson and binomial distributions. Besides, we introduce prior distributions, gamma, and beta distributions, conjugated with these discrete distributions. The Bayesian method is applied for updating the parameters of the model as this approach yields bonus-malus premiums. We use a real example data to demonstrate the model. The randomized neighborhood search (RNS) technique is introduced for estimating the parameters to minimize the statistical value for Akaike’s Information Criterion (AIC). This methodology allows us to obtain a good fit to the data set considered.