Insurance Pricing Research Articles

Drought disaster risk assessment and yield insurance pricing of maize: a case study of Liaoning Province, China

Starting from the ‘four-factors’ theory of natural disaster risk formation, the study first selects indices that represent hazard, vulnerability, exposure, and emergency response and recovery capability to construct the drought risk assessment index system. Then the natural disaster risk index method is employed to evaluate the risk of maize drought disasters in Liaoning. Finally, the pure premium rate for maize yield insurance is determined based on the risk assessment results and the Copula function. The results show that: (1) The hazard, vulnerability, and exposure index in northwestern Liaoning are high, while emergency response and recovery capability is relatively low. Therefore, northwestern Liaoning is identified as a high-risk area for drought risk. (2) There exists a negative correlation between the drought risk index and maize yield in most areas of Liaoning; that is, higher drought risk is associated with lower maize yield. (3) Under the same coverage level, pure rates are higher in the northwestern and eastern Liaoning and relatively lower in the southwestern and southeastern Liaoning. Under different coverage levels, higher coverage corresponds to increased pure rates. The results can offer valuable guidance and benchmarks for relevant departments in Liaoning Province to assess the impact of drought risk on agriculture.

Features to Involve and Collect in Future Auto Insurance Pricing

The property insurance industry is a highly data-driven sector. In the traditional model, insurance pricing largely depends on the self-reported risk characteristics of clients, such as age, gender, vehicle type, etc. These characteristics help insurance companies categorize clients into different risk levels and set premiums accordingly. With the development of telematics, insurance companies can now collect and analyze more dynamic data that is more directly related to risk. This study presents a comprehensive analysis of three feature selection models for vehicle insurance pricing. Utilizing regression techniques, it evaluated a multitude of factors believed to influence claim frequency and severity. Through a rigorous comparative study, key factors that significantly impact the vehicle are assessed and fit to different regression models. The articles findings indicate that factors such as policy bonus, mileage base data, and car usage are paramount in determining insurance rates. Moreover, the study revealed that incorporating these factors into the pricing model enhances its accuracy and fairness.

Analyzing the Influence of Telematics-Based Pricing Strategies on Traditional Rating Factors in Auto Insurance Rate Regulation

This study examines how telematics variables such as annual percentage driven, total miles driven, and driving patterns influence the distributional behaviour of conventional rating factors when incorporated into predictive models for capturing auto insurance risk in rate regulation. To effectively manage the complexity inherent in telematics data, we advocate for the adoption of non-negative sparse principal component analysis (NSPCA) as a structured approach for data dimensionality reduction. By emphasizing sparsity and non-negativity constraints, NSPCA enhances the interpretability and predictive power of models concerning both loss severity and claim counts. This methodological innovation aims to advance statistical analyses within insurance pricing frameworks, ensuring the robustness of predictive models and providing insights crucial for rate regulation strategies specific to the auto insurance sector. Results show that, to enhance auto insurance risk pricing models, it is essential to address data dimension reduction challenges when integrating telematics data variables. Our findings underscore that integrating telematics variables into predictive models maintains the integrity of risk relativity estimates associated with traditional policy variables.

ПРОБЛЕМИ ТА ПЕРСПЕКТИВИ СТРАХУВАННЯ ТУРИСТИЧНОЇ ДІЯЛЬНОСТІ

The article discusses the types of insurance in tourism. Based on the analysis of the insurance market of Ukraine, it was established that the number of insurance companies decreased by almost three times during the years 2015-2022, and 25 insurance companies worked in the field of tourism in 2023. It was revealed that the following companies are the leaders in the travel insurance market: European Travel Insurance, ARX, VUSO, PZU Ukraine. The factors that hold back the development of tourism insurance are highlighted: military actions due to Russia's invasion of Ukraine, political instability; decrease in the number of tourists, low solvency of the population; imperfect legal framework; poor awareness of the population in the field of tourism insurance; public distrust of insurance companies; a narrow range of insurance services in the field of tourism insurance; incomplete and untimely fulfillment of obligations to policyholders; limited scope of insurance protection due to reduction of insurance prices by insurers; decrease in the quality of insurance products; insufficient professional level of insurance company specialists; overall low development of the country's insurance market. The main trends in the field of insurance in Ukraine are revealed: individual policies for certain tourist segments, use of artificial intelligence, transformation of products into the format of electronic policies, blockchain technologies. Directions for solving problems in the field of insurance in tourism are indicated: improvement of the regulatory and legal framework; ensuring political stability, increasing economic development in the state; training of highly qualified personnel in the field of insurance; improvement of insurance culture; creation of protective mechanisms for tourists; assistance from the state to the development of the insurance market in Ukraine; improvement of the risk management mechanism; increasing public trust in insurance companies; expanding the list of insurance services and improving their quality.

Ordered Lorenz Regularization (OLR): A General Method to Mitigate Overfitting in General Insurance Pricing via Machine Learning Algorithms

When machine learning algorithms are used to determine the price of general insurance, they can sometimes overfit the data. This overfitting can lead to problems for both customers and insurance companies. To address this issue, we’ve developed a new approach called Ordered Lorenz Regularization (OLR). We have tested OLR on general insurance data. The results have demonstrated that OLR is successful in reducing overfitting. Additionally, when we use OLR for pricing general insurance, it helps establish the lowest and highest possible premiums.

A novel Bayesian Pay-As-You-Drive insurance model with risk prediction and causal mapping

The modern vehicle insurance industry is increasingly adopting Pay-As-You-Drive (PAYD) insurance models, aligning premium costs with driving behavior. Our study introduces a Bayesian approach to PAYD insurance, leveraging the strengths of Naive Bayes classifiers and Bayesian Networks to handle uncertainty and integrate prior knowledge in risk assessment. The Naive Bayes model achieved an 87.5% accuracy in predicting risk partitions. With the Bayesian Network providing insights into causal relationships through a Directed Acyclic Graph (DAG), we also address the challenges of traditional actuarial models — low interpretability of intra-factor relationships and thus hard to plan for risk management for both provider and policyholder. Our research contributes to optimizing insurance pricing strategies. Still, the causal mapping also dismisses the meaningfulness of using geographic grouping in insurance pricing (discriminatory or not). It reassures the theoretical advantage of the PAYD model over the traditional model, facilitating access to affordable coverage for policyholders.

Modelling of Claim and Pricing of Motor Insurance Based on Bonus-Malus System Considering the Frequency and Severity of Claims

This article proposes new distributions for claim frequency and severity, specifically tailored for a bonus-malus system in automobile insurance. The mixed Poisson with weighted quasi Lindley distribution is recommended for modeling claim frequency, while the mixed exponential with weighted quasi Lindley distribution is suggested for modeling claim severity. To estimate insurance premiums, the Bayesian method is employed, incorporating both frequency and severity distributions. The study validates the proposed models using real data from an Australian insurance company, which includes 67,856 policies. The assessment of model adequacy indicates that the Poisson-weighted quasi Lindley distribution is a suitable fit for modeling claim frequency, while the exponential-weighted quasi Lindley distribution is appropriate for modeling claim severity. Overall, the results suggest that the proposed models offer optimal premium estimations, considering both claim frequency and severity, which can lead to fairer pricing and increased customer appeal during claim occurrences compared to conventional models.

Pricing models for small and micro loan portfolio insurance

From the perspective of the insurance deductible, this article constructs pricing models suitable for small and micro loan portfolio insurance under realistic conditions, and summarizes relevant pricing laws through examples. It is found that the option attribute of loan portfolio insurance contracts endowed by absolute or relative deductible clause can be used to price small and micro loan portfolio insurance. Meanwhile, owing to the offset effect of the loan portfolio on the credit risk of different single loans, the premium rate of loan portfolio insurance should be controlled between that of corresponding single loan insurance. Moreover, properly adjusting the deductible ratio, insurance period, and composition of the insured loan portfolio can create more space for reducing the insurance price of the loan portfolio or expanding insurance profits. Our study improves the pricing model system of small and micro loan insurance, which has important theoretical value and practical significance for the scientific pricing of loan portfolio insurance.

Impact of Ecological Cognitive Bias on Pesticide Reduction by Natural Rubber Farmers in China: Insight from Price Insurance Satisfaction

Some natural rubber farmers mistakenly equate the ecological functions of rubber plantations with those of primary forests. This cognitive bias can hinder pesticide reduction efforts. Meanwhile, natural rubber farmers gain security through price insurance, which helps them adopt a long-term perspective on environmental protection, mitigating the negative impact of cognitive biases on pesticide use decisions. However, existing research often overlooks the influence of ecological cognitive bias on pesticide reduction and the moderating role of price insurance satisfaction. This study utilizes field survey data from Hainan and employs logit models and double machine learning models to empirically analyze the impact of ecological cognitive bias on pesticide reduction among natural rubber farmers. It further tests the underlying mechanisms using moderation models. The results indicate that (1) ecological cognitive bias negatively affects pesticide reduction among natural rubber farmers, and (2) price insurance satisfaction mitigates the impact of ecological cognitive bias on pesticide reduction. Based on these findings, the government should enhance education and training to raise ecological awareness among natural rubber farmers and reduce ecological cognitive biases. Disseminating knowledge about price insurance and establishing a comprehensive insurance system can secure farmers’ income and promote the rational use of pesticides.

Advancements in predictive modeling for insurance pricing: Enhancing risk assessment and customer segmentation

Advancements in predictive modeling for insurance pricing: Enhancing risk assessment and customer segmentation

Health Insurance Factor Analysis

This paper explores the intricacies of health insurance costs in the United States, emphasizing the Affordable Care Act's (ACA) role in reform. Employing a "health insurance factor analysis" approach, the study identifies key determinants using data visualization and regression models. Factors such as age, BMI, family size, gender, smoking status, and geographic region significantly influence insurance prices. The research evaluates various regression models and neural networks, with linear regression standing out for its high accuracy. The findings underscore the impact of smoking, medical history, and coverage level on insurance costs. Despite dataset limitations and sample size considerations, this study contributes to a nuanced understanding of health insurance pricing, aiding insurers, policymakers, and individuals in decision-making. By integrating data insights and predictive models, the research advances comprehension of the complex relationships shaping health insurance costs. The ultimate goal is to optimize insurance programs and promote accessible and affordable health insurance for all.

Research on Changes in Travel Insurance Premiums Driven by Climate Change: A Case Study of Hong Kong Region

This research aims to study the impacts of climate change on worldwide general travel insurance in Hong Kong and to provide a scientific basis for premium pricing strategies in a climate-driven context. The study adopts both qualitative and quantitative research methods to reveal the relationship between climate change and travel insurance. The qualitative analysis part constructs a theoretical framework through literature review. Taking into account the current state of research, the impact of climate change on the demand for travel insurance as well as the challenges and opportunities of premium pricing strategies are discussed in depth. The quantitative analysis section collected data on flights at the Hong Kong International Airport (departures, delays, and cancellations) and travel insurance claim occurrence. The weather conditions were also checked through the weather website to analyze the correlation between climate factors and insurance claims. The findings indicated that climate change has a significant impact on the demand for travel insurance, especially during the prolonged rainy season in Hong Kong, when extreme weather events lead to an increased risk of cancellation or delay of travel plans. Meanwhile, the quantitative analysis results demonstrated a significant correlation between weather factors and flight status and insurance occurrence, which provided empirical evidence for risk assessment and premium pricing of worldwide travel insurance in Hong Kong.

Real Estate Location Optimization Model Based on Linear Programming Model Mombined with Property Insurance Pricing

Real Estate Location Optimization Model Based on Linear Programming Model Mombined with Property Insurance Pricing

EXPRESS: How Insurance Prices Affect Consumers’ Purchase Decisions: Insurance Price as a Risk Signal

Retailers, service providers, and manufacturers have discovered that complementary optional insurance is an attractive source of profit and frequently charge substantial insurance prices compared to the price of the product to be insured. The implicit assumption behind this pricing strategy is that product purchase decisions are independent of the insurance offer. The authors question this assumption and propose that consumers interpret the price of insurance as a risk signal with respect to the underlying product. Perceived risk, in turn, negatively affects consumers’ decision to purchase the product in a given purchase situation. The results of a survey, three online experiments, and two studies using transactional data provide evidence for the proposed insurance price risk signal. The findings reveal that perceived risk mediates the link between the relative insurance price level and consumers’ decision to purchase the underlying product. Offering other optional add-ons and providing objective risk information weakens the insurance price risk signal.

MEDICAL INSURANCE COST ANALYSIS AND PREDICTION USINGEXTREME GRADIENT BOOSTING ALGORITHM

An insurance policy lowers or completely removes the costs related to declining returns caused by different risks. A variety of things affect the cost of insurance. These elements have an impact on how insurance plans are made. In the insurance industry, machine learning (ML) has promise for increasing the effectiveness of insurance policy terms. Actual modelling of insurance claims has emerged as a major field of study in the health insurance industry in recent years, primarily for the purpose of determining appropriate rates. This is essential for drawing in new insured’s, keeping the ones you already have, and managing current plan participants well. However, it can be difficult to create an accurate forecast model for medical insurance prices because of the multitude of factors that influence them and their inherent complexities. The expected costs of health insurance could be greatly impacted by a number of factors, such as provider characteristics, lifestyle decisions, health status, accessibility in a given area, and demographic information. Actuarial research into predictive modeling in healthcare is still going strong, as more insurance companies look to leverage ML technologies to increase productivity and efficiency. Regression-based ensemble machine learning models that incorporate different Extreme Gradient Boosting (XGBoost) techniques are used in this study to forecast medical insurance expenses.

Convex and Lorenz orders under balance correction in nonlife insurance pricing: Review and new developments

By exploiting massive amounts of data, machine learning techniques provide actuaries with predictors exhibiting high correlation with claim frequencies and severities. However, these predictors generally fail to achieve financial equilibrium and thus do not qualify as pure premiums. Autocalibration effectively addresses this issue since it ensures that every group of policyholders paying the same premium is on average self-financing. Balance correction has been proposed as a way to make any candidate premium autocalibrated with the added advantage that it improves out-of-sample Bregman divergence and hence predictive Tweedie deviance. This paper proves that balance correction is also beneficial in terms of concentration curves and derives conditions ensuring that the initial predictor and its balance-corrected version are ordered in Lorenz order. Finally, criteria are proposed to rank the balance-corrected versions of two competing predictors in the convex order.

Navigating Health Insurance Economics: A Data-Driven Approach to Enhanced Pricing in the United States

This study delves into the dynamics of healthcare spending in the United States, revealing a considerable financial commitment that hasn't translated into commensurate health outcomes. With healthcare costs reaching $4.3 trillion in 2021, driven by factors such as an aging population and escalating service prices, the nation confronts challenges to its fiscal health. The analysis extends to the intricacies of U.S. health insurance pricing, critiquing the existing system's complexity and opacity while drawing comparisons with approaches in other developed countries. Amid criticisms of profit-centric motives in the private sector, the study prompts discussions on potential reforms, learning from international experiences. Additionally, the study explores the transformative potential of data analytics in health insurance pricing, emphasizing its role in enhancing fairness and competitiveness. However, ethical considerations, including privacy, data security, and potential biases, underscore the need for a delicate balance between leveraging data-driven insights and responsible practices. The results of the study may be of great interest to specialists from the point of view of the further development of the compulsory social health insurance system in the Republic of Kazakhstan.

On the cost of risk misspecification in insurance pricing

In the non-life insurance industry, pricing is often done relative to individual criteria of policyholders. Various classification algorithms are in use to categorize policyholders into risk classes defined by the insurer, but classification errors may result from this process. In the light of recent automatic classification practices, it becomes important to assess the risks caused by such errors. In this paper we examine the impact of risk class misspecifications for a simple situation with two risk types. We provide a mean-variance framework for quantitatively studying the insurer’s optimization problem of specifying premiums and we analyze the tradeoff of costs and benefits when classification error probabilities are known.

What is fair? Proxy discrimination vs. demographic disparities in insurance pricing

Discrimination and fairness are major concerns in algorithmic models. This is particularly true in insurance, where protected policyholder attributes are not allowed to be used for insurance pricing. Simply disregarding protected policyholder attributes is not an appropriate solution as this still allows for the possibility of inferring protected attributes from non-protected covariates, leading to the phenomenon of proxy discrimination. Although proxy discrimination is qualitatively different from the group fairness concepts discussed in the machine learning and actuarial literature, group fairness criteria have been proposed to control the impact of protected attributes on the calculation of insurance prices. The purpose of this paper is to discuss the relationship between direct and proxy discrimination in insurance and the most popular group fairness axioms. We provide a technical definition of proxy discrimination and derive incompatibility results, showing that avoiding proxy discrimination does not imply satisfying group fairness and vice versa. This shows that the two concepts are materially different. Furthermore, we discuss input data pre-processing and model post-processing methods that achieve group fairness in the sense of demographic parity. As these methods induce transformations that explicitly depend on policyholders' protected attributes, it becomes ambiguous whether direct and proxy discrimination is, in fact, avoided.

On duration effects in non-life insurance pricing

The paper discusses duration effects on the consistency of mean parameter and dispersion parameter estimators in exponential dispersion families (EDFs) that are the standard models used for non-life insurance pricing. Focus is on the standard generalised linear model assumptions where both the mean and variance, conditional on duration, are linear functions in terms of duration. We derive simple convergence results that highlight consequences when the linear conditional moment assumptions are not satisfied. These results illustrate that: (i) the resulting mean estimators always have a relevant asymptotic interpretation in terms of the duration adjusted actuarially fair premium—a premium that only agrees with the standard actuarial premium using a duration equal to one, given that the expected value is linear in the duration; (ii) deviance based estimators of the dispersion parameter in an EDF should be avoided in favour of Pearson estimators; (iii) unless the linear moment assumptions are satisfied, consistency of dispersion and plug-in variance estimators can not be guaranteed and may result in spurious over-dispersion. The results provide explicit conditions on the underlying data generating process that will lead to spurious over-dispersion that can be used for model checking. This is illustrated based on real insurance data, where it is concluded that the linear moment assumptions are violated, which results in non-negligible spurious over-dispersion.