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Critical illness insurance protects against complex risks and high medical costs. This study proposes a premium model using a modified call option framework, where benefits are paid if medical expenses exceed a predefined claim limit. 'We examine two cases based on Indonesia's National Health Insurance regulations: with and without an inpatient care class upgrade. The model employs the Gamma process to represent treatment costs and claim limits while analyzing the impact of parameters on insurance premiums. Results show that premiums increase with the cost-to-claim limit ratio in the non-upgraded model. In contrast, in the upgraded model, premiums rise as the claim limit increases, assuming expected costs exceed the limit.

Designing fair and sustainable pricing mechanisms for health insurance requires accurate risk assessment and the formulation of incentive-compatible strategies among stakeholders. This study proposes a hybrid framework that integrates machine learning with game theory to determine optimal, risk-based premium rates. Using a comprehensive dataset of insured individuals, the XGBoost algorithm is employed to predict medical claim costs and calculate corresponding premiums. To enhance transparency and explainability, SHAP analysis is conducted across four risk-based groups, revealing key drivers, including healthcare utilization and demographic features. The strategic interactions among the insurer, insured, and employer are modeled as a repeated game. Using the Folk Theorem, the conditions under which long-term cooperation becomes a sustainable Nash equilibrium are explored. The results demonstrate that XGBoost achieves high predictive accuracy (R2 ≈ 0.787) along with strong performance in error measures (RMSE ≈ 1.64 × 107 IRR, MAE ≈ 1.08 × 106 IRR), while SHAP analysis offers interpretable insights into the most influential predictors. Game-theoretic analysis further reveals that under appropriate discount rates, stable cooperation between stakeholders is achievable. These findings support the development of equitable, transparent, and data-driven health insurance systems that effectively align the incentives of all stakeholders.

We propose a generalized Cramér–Lundberg model of the risk theory of non-life insurance and study its ruin probability. Our model is an extension of that of Dubey (1977) to the case of multiple insureds, where the counting process is a mixed Poisson process and the continuously varying premium rate is determined by a Bayesian rule on the number of claims. We use two proofs to show that, for each fixed value of the safety loading, the ruin probability is the same as that of the classical Cramér–Lundberg model and does not depend on either the distribution of the mixing variable of the driving mixed Poisson process or the number of claim contracts.

The National Flood Insurance Program (NFIP) is housed within the Federal Emergency Management Agency (FEMA) and offers insurance policies that are marketed and sold through private insurers, but with the risks borne by the U.S. federal government. NFIP's primary goals are to ensure affordable insurance premiums, secure widespread community participation in the program, and earn premium and fee income that covers claims paid and program expenses over time. In July 2012, the U.S. Congress passed the Biggert-Waters Flood Insurance Reform and Modernization Act (Biggert-Waters 2012), designed to move toward an insurance program with NFIP risk-based premiums that better reflected expected losses from floods at insured properties. This eliminated policies priced at what the NFIP called \"pre-FIRM subsidized\" and \"grandfathered.\" As Biggert-Waters 2012 went into effect, constituents from multiple communities expressed concerns about the elimination of lower rate classes, arguing that it created a financial burden on policy holders. In response to these concerns Congress passed The Homeowner Flood Insurance Affordability Act of 2014 (HFIAA 2014). The 2014 legislation changed the process by which pre-FIRM subsidized premiums for primary residences would be removed and reinstated grandfathering. As part of that legislation, FEMA must report back to Congress with a draft affordability framework. Affordability of National Flood Insurance Program Premiums: Report 1 is the first part of a two-part study to provide input as FEMA prepares their draft affordability framework. This report discusses the underlying definitions and methods for an affordability framework and the affordability concept and applications. Affordability of National Flood Insurance Program Premiums gives an overview of the demand for insurance and the history of the NFIP premium setting. The report then describes alternatives for determining when the premium increases resulting from Biggert-Waters 2012 would make flood insurance unaffordable.

In Europe, climate change has a big impact on agriculture, due to an increase in the frequency and severity of extreme weather events. Many and prolonged droughts, heatwaves, floods, and hailstorms cause major economic losses that affect crop quality and generate instability in supply chains. In this study, we analyse the evolution of extreme weather events across Europe starting from the 1980s. The economic losses caused by extreme events were divided into three categories: heatwaves, frost, and fires; floods; and storms. In order to identify the trend and any shifts of the trend of the extreme weather events, we calculated moving averages over different periods: 5, 10, 20, and 30 years. The moving average analysis shows how climate change has altered from causing isolated and temporary economic losses to generate a consistent upward trend in losses, with an increasingly significant impact in the short, medium, and long term. In the second part of this study, we conducted a correlation analysis between the economic losses caused by extreme weather events and variations in property insurance premiums (fire and other property damage—which includes crop insurance premiums) and we calculated correlation coefficients directly, with a one-year lag, and with a two-year lag. Thus, we analysed whether insurance markets respond immediately to incurred losses or whether, depending on climate trends, there are delays in premium adjustments.

Usage-Based Insurance (UBI), also referred to as telematics-based insurance, has been experiencing a growing global diffusion. In addition to being well established in countries such as Italy, the United States, and the United Kingdom, UBI adoption is also accelerating in emerging markets such as Japan, South Africa, and Brazil. In Japan, telematics insurance has shown significant growth in recent years, with a steadily increasing subscription rate. In South Africa, UBI adoption ranks among the highest worldwide, with market penetration placing the country among the top three globally, just after the United States and Italy. In Brazil, UBI adoption is expanding, supported by government initiatives promoting road safety and innovation in the insurance sector. According to a MarketsandMarkets report of February 2025, the global UBI market is expected to grow from USD 43.38 billion in 2023 to USD 70.46 billion by 2030, with a compound annual growth rate (CAGR) of 7.2% over the forecast period. This growth is driven by the increasing adoption of both electric and internal combustion vehicles equipped with integrated telematics systems, which enable insurers to collect data on driving behavior and to tailor insurance premiums accordingly. In this paper, we analyze a large dataset consisting of trips recorded over five years from 100,000 policyholders across the Italian territory through the installation of black-box devices. Using univariate and multivariate statistical analyses, as well as Generalized Linear Models (GLMs) with Zero-Inflated Poisson distribution, we examine claims frequency and assess the relevance of various synthetic indicators of driving behavior, with the aim of identifying those that are most significant for insurance pricing.

This study investigated the nexus among the profitability, sales, and willingness to pay (WTP) more for weather index-based agricultural insurance premiums of flower farmers. In addition, the effect of sociodemographic and farm characteristics of flower farmers on their WTP more for insurance premiums was also estimated. A total of 160 flower farmers were selected from Bangladesh using the purposive random sampling technique. Propensity score matching technique was employed to identify the sales difference depending on WTP for insurance premiums while the profitability differences of flower farmers were assessed from different points of view. A binary logistic regression model was used to estimate the effect of sociodemographic and farm characteristics of flower farmers on their WTP more for insurance premiums, while a Likert scale was used to identify the major problems faced by flower farmers. Flower growers are willing to pay a higher premium for insurance when their sales decline. Farmers with lower profitability show a greater WTP higher insurance premiums, whereas those with relatively higher profitability are less inclined to do so. Farmers’ WTP more for insurance premiums decreases with age, education, and farm area, while farmers’ WTP more for insurance premiums increases with experience, training, earning members, marigold farming, and consciousness about natural calamities, pests, and diseases. The most significant problems faced in flower production are high input costs, demand fluctuation, pest and disease attacks, price fluctuation, and loss of production. Thus, the introduction of crop insurance in flower farming may increase profitability and reduce the exposure to risks involved in flower farming. The involvement of younger and more trained farmers in flower farming will increase their WTP more for insurance premiums.

Specialist groups have often advised health ministers and other decision makers in developing countries on the use of social health insurance (SHI) as a way of mobilizing revenue for health, reforming health sector performance, and providing universal coverage. This book reviews the specific design and implementation challenges facing SHI in low- and middle-income countries and presents case studies on Ghana, Kenya, Philippines, Colombia, and Thailand.

We adopt a systemic risk indicator measured by the price of insurance against systemic financial distress and assess individual banks’ marginal contributions to the systemic risk. The methodology is applied using publicly available data to the 19 bank holding companies covered by the U.S. Supervisory Capital Assessment Program (SCAP), with the systemic risk indicator peaking around $1.1 trillion in March 2009. Our systemic risk contribution measure shows interesting similarity to and divergence from the SCAP loss estimates under stress test scenarios. In general, we find that a bank’s contribution to the systemic risk is roughly linear in its default probability but highly nonlinear with respect to institution size and asset correlation.

This paper investigates an optimal reinsurance policy using a risk model with dependent claim and insurance premium by assuming that the insurance premium is random. Their dependence structure is modeled using Sarmanov's bivariate exponential distribution and the Farlie-Gumbel-Morgenstern (FGM) copula-based bivariate exponential distribution. The reinsurance premium paid by the insurer to the reinsurer is fixed and is charged by the expected value premium principle (EVPP) and standard deviation premium principle (SDPP). The main objective of this paper is to determine the proportion and retention limit of the optimal combination of proportional and stop-loss reinsurance for the insurer. Specifically, with a constrained reinsurance premium, we use the minimization of the Value-at-Risk (VaR) of the insurer's net cost. When determining the optimal proportion and retention limit, we provide some numerical examples to illustrate the theoretical results. We show that the dependence parameter, the probability of claim occurrence, and the confidence level have effects on the optimal VaR of the insurer's net cost.