Agricultural production is highly vulnerable to weather variability, necessitating robust risk management strategies such as weather index insurance (WII). While WII has shown potential to mitigate weather-related risks, its adoption faces significant challenges due to basis risk and the complexity of index-based payout structures. This article proposes an integrated design framework for WII, grounded in expected utility maximization, to address these issues. The framework leverages a tree-based sequential quadratic programming algorithm to simultaneously select relevant weather variables and payout structures. By optimizing model performance under a controlled level of model complexity, our approach enhances the interpretability and effectiveness of WII contracts. The empirical study, applied to soybean production in Iowa, demonstrates that the proposed design significantly improves policyholder utility, even without government subsidies, and outperforms traditional methods including least absolute shrinkage and selection operator (LASSO), principal component analysis (PCA), and stepwise regression. These findings offer valuable insights for improving the agricultural insurance market and fostering wider adoption of WII.
The health insurance industry experienced substantial consolidation following the passage of the Affordable Care Act (ACA). We use event studies and cross-sectional regression models to measure the effects the ACA had on health insurer mergers and acquisitions. Generally, our analyses document positive target returns and nonnegative bidder and combined returns, which provide support for the value maximization hypothesis. We also find that medical loss ratio (MLR) rebates and Medicaid expansion both influence merger activity in the industry, while exchange participation has no significant effect. Additionally, our results indicate mergers occur for synergistic reasons in the pre-ACA period, while post-ACA mergers have broadly collusive and noncompetitive effects. However, we find that rival firms participating in the exchanges experience negative returns surrounding merger announcements, suggesting a more competitive market in the exchanges.
Customers of pension plans often rely on financial advice to make investment decisions. This article proposes a pension plan design that improves both optimization and communication of retirement savings. Unlike conventional approaches, we advocate setting only an upper limit on desired income in the payout phase, while allowing the allocation to risky assets to remain unconstrained. Simulation results show that this design stabilizes both the average and volatility of pension payouts without imposing inefficient restrictions on early investment choices. To enhance client understanding, we introduce a set of decision criteria for retirement drawdowns that supports simple, intuitive interaction and builds trust. Our approach is fully implementable in artificial intelligence (AI)-driven wealth management systems, enabling fintech applications to guide clients effectively and assisting human advisors in providing better, data-driven insights. The proposed framework balances risk-adjusted returns and client comprehension, offering a practical, evidence-based solution for improving long-term retirement outcomes.
This article investigates optimal lifetime consumption, investment, and life insurance decisions in a continuous framework. We incorporate a progressive estate tax and a tax-exempt life insurance market, which leads to the nondifferentiability of the utility function for bequest at the n-th tax tier threshold. Progressive estate taxation together with a tax-exempt life insurance market introduces nonlinearity in the relationship between wealth and life insurance proceeds, thereby rendering the elegant martingale and duality methods inapplicable. Consequently, we employ the Legendre transform to derive explicit expressions for the optimal strategies. Our analysis reveals that the estate tax reduces the incentive to save while increasing the demand for life insurance, as life insurance serves as an alternative to direct inheritance for intergenerational wealth transfer. Most notably, the estate tax exerts a dual effect on consumption and investment, driven by both substitution and income effects. Specifically, the estate tax stimulates consumption and reduces investment for agents with high elasticity of intertemporal substitution (EIS), whereas it suppresses consumption and incentivizes investment for those with low EIS.
This article examines the optimal investment-consumption problem with a tax-favored private defined-contribution pension scheme, which both encourages participation and allows investment in risky assets within the pension account. The framework incorporates not only individuals' regular investment and consumption decisions but also their pension contributions and pension investment choices. To capture the role of tax-favored policy, we introduce a general income tax function, and within a two-account setting, derive analytical solutions under constant relative risk-aversion (CRRA) utility using the martingale approach. We then discuss how the tax-favored pension scheme encourages participation in detail. Numerical simulations based on real-world data in China are conducted, which illustrate the effects of different parameters and enable a comparison with the Merton model. Several practical policy implications are discussed to improve the effectiveness of tax-favored pension schemes.
The Wishart-gamma random effects model, introduced by Denuit and Lu in 2021, is both flexible and tractable for a variety of insurance applications such as multiperil ratemaking, frequency-severity ratemaking, and microreserving. However, so far, this model has yet to be applied in either the statistical or the actuarial literature, and one important challenge is that its pricing and likelihood formulas involve a high-dimensional determinant as well as its derivatives. This article fills this gap and introduces appropriate tools to deal with such derivatives and applies them to multiperil ratemaking. More precisely, we use matrix differential calculus to simplify the pricing formula, the principal minor assignment to analyze the model identification, and the composite likelihood for model estimation. We use simulated data to illustrate the effectiveness of our method and estimate the model on a real multiperil insurance claim dataset.
Two goals of the Affordable Care Act (ACA) were to decrease the complexity of health insurance and to create transparent marketplaces. Using U.S. health insurer data from 1996-2021, we examine whether these reforms strengthened market discipline. We find clear evidence of baseline discipline: Insurers with weaker financial ratings command lower prices and sell fewer policies. We find no evidence of a broad, market-wide strengthening post ACA. Using a triple-difference research design, however, we show that exchange-participating insurers experienced a significant increase in price-based discipline after ACA implementation, with rating downgrades associated with substantially larger reductions in pricing power for exchange firms than for non-exchange firms in the post-ACA period. Quantity discipline did not strengthen on exchanges, a pattern consistent with the inelastic demand created by premium subsidies. Group markets exhibit weaker quantity-based discipline than nongroup markets. Our results suggest that regulatory transparency initiatives can meaningfully enhance market discipline in the segments where information gains are most actionable.
To better understand household behavior in consumption, investment, and life insurance, this article develops an optimal decision-making model for a two-person household. Extending the classic individual life-cycle framework, the model incorporates joint decisions on consumption and habit formation to reflect the nature of household financial planning. The problem is decomposed into three standard optimal control subproblems and solved using Hamilton-Jacobi-Bellman equations. Assuming constant relative risk aversion (CRRA) utility, we derive analytical solutions for the optimal strategy. Similar to the individual setting, the household's optimal consumption, life insurance, and investment decisions are linear functions of total available capital, which includes current wealth, human capital, and reserves for habitual consumption. Numerical examples show that habit formation tends to reduce both insurance expenditures and investments. Moreover, households with weaker path dependence in consumption history, and thus greater adaptability to changing circumstances, can achieve smoother consumption trajectories.
We use the dynamic inoperability input-output model-presented in this journal to analyze cyber risk scenarios-to evaluate the economic impact of seven plausible, potentially high-consequence artificial intelligence (AI) risk scenarios. The scenarios span a diverse range of AI-related disruptions, including failures of widely used business software, breakdowns in AI-enabled transport systems, or targeted AI-based attacks on critical infrastructure. Each scenario is modeled based on sectoral inoperability, recovery dynamics, and cascading effects across the economy. Estimated losses for the U.S. economy range from US$11 billion to US$85 billion. While most scenarios fall within insurable limits, some might exceed the risk-bearing capacity of private insurers and require public-private risk-sharing mechanisms, especially for AI-based attacks on critical infrastructure. This study presents a structured, scenario-based approach to assessing the insurability of emerging AI risks in the absence of historical data and thus assists decision-makers in better understanding this emerging type of risk.
We develop an optimization model that minimizes basis risk in weather index insurance for Ontario's diverse climatic regions, while integrating regularization terms that address extreme temperature variations and impose spatial regularity in strike temperatures across nearby weather stations. By hybridizing genetic algorithm with the Nelder-Mead algorithm, we determine location-specific strike temperatures that accurately reflect local conditions and minimize basis risk. The results from the study show that accounting for spatial regularity and extreme weather improves both the fairness and accuracy of payoffs, thereby reducing mismatches between insured losses and compensation. While geographic factors such as longitude, latitude, distance, and altitude are key determinants of optimal contract design, their impact differs from year to year. These findings underscore the importance of locally adapted index insurance and dynamic parameter updates in response to shifting weather patterns. The contribution lies in the optimization model's design, which enhances the fairness, resilience, and practical reliability of weather index insurance under climate variability. Generally, the proposed framework strengthens the practical reliability of weather index insurance as a risk management tool for farmers in the face of climate variability.
Optimal decumulation of a Defined Contribution (DC) pension plan can be viewed as a problem in optimal stochastic control, which requires specification of an objective function, a combination of reward and risk. An intuitive specification of reward is the sum of withdrawals over the retirement period. This article investigates three tail risk measures for running out of savings in a DC plan decumulation strategy, which includes (i) expected shortfall, (ii) linear shortfall, and (iii) probability of shortfall. From the perspective of all optimal solutions, we establish that, under suitable regularity assumptions, the set of optimal controls corresponding to all expected reward expected shortfall Pareto efficient frontier curves is identical to the set of optimal controls associated with all expected reward and linear shortfall Pareto efficient frontier curves. To better understand the impact of a chosen risk measure, we compare its optimal controls across all three combinations of risk measures and reward performance criteria, while fixing the values of the risk aversion and wealth/probability level parameters at reasonable levels. This comparison reveals a clear preference for the linear shortfall risk measure, which yields more desirable optimal strategies. From a practical point of view, we show that allowing variable withdrawals has a large effect on reducing risk, compared to dynamic asset allocation.
The rapid growth in healthcare expenditures in China over recent decades can be partially attributed to outpatient inefficiencies in risk-sharing and the lack of effective mutual aid mechanisms, which have driven overutilization of inpatient services. This study investigates the impact of China's outpatient mutual aid policy on inpatient medical expenditures. Exploiting a quasi-experimental design centered on outpatient mutual aid reform, we employ a difference-in-difference (DiD) methodology to analyze the policy effect. Our analysis, which utilizes inpatient medical records, demonstrates that the mutual aid policy significantly reduces total inpatient costs and out-of-pocket expenditures. This effect is particularly significant in cases involving ambulatory care-sensitive conditions (ACSCs), highlighting the potential for primary care to prevent unnecessary hospital admissions. Furthermore, our findings suggest that the magnitude of expenditure reductions is more substantial among older patients, particularly those seeking treatment in tertiary hospitals. Our projections further reveal that while the reform leads to a net increase in overall medical expenses through enhanced outpatient utilization, this growth is fiscally sustainable and reflects improved healthcare access rather than inefficient spending.
The Financial Accounting Standards Board (FASB) issued Accounting Standards Update No. 2016-01, which requires firms to report unrealized gains and losses on available-for-sale (AFS) equity securities in net income. Previously, these gains and losses were reported in other comprehensive income and were not recognized in net income until the investments were sold. The rule change begs the question of whether insurers increased their earnings management discretion (largely via loss reserves) to offset the reduced discretion in terms of recognizing investment income. We examine how earnings reclassification impacts firms' investment strategy and earnings management behavior around earnings reports. Using data from U.S. insurers, we find that firms decrease their equity holdings while increasing holding periods on equity securities following the adoption of this new standard. These results suggest that ASU 2016-01 shifts firms' investment focus from short-term financial reporting to long-term investment income maximization goals. We also find evidence that this rule update changes firms' earnings management behavior in that the rule change removes firms' incentives to cherry-pick sales of equity. We document that public insurers are involved in less gains trading to avoid reporting losses following the rule adoption. Instead, we find evidence that public insurers are more likely to use discretion over reported loss reserves as opposed to gains trading to manage reported earnings after the rule change.
The growing number of infectious disease outbreaks, like the one caused by the SARS-CoV-2 virus, underscores the necessity of actuarial models that can adapt to epidemic-driven risks. Traditional life insurance frameworks often rely on static mortality assumptions that fail to capture the temporal and behavioral complexity of disease transmission. In this paper, we propose an integrated actuarial framework based on the SEIARD epidemiological model. This framework enables the explicit modeling of incubation periods and disease-induced mortality. We derive key actuarial quantities, including the present value of annuity benefits, payment streams, and net premiums, based on SEIARD dynamics. We formulate a prospective reserve function and analyze its evolution throughout the course of an epidemic. Additionally, we examine the forces of infection, mortality, and removal to assess their impact on epidemic-adjusted survival probabilities. Numerical simulations implemented via a nonstandard finite difference (NSFD) scheme illustrate the model's applicability under various parameter settings and insurance policy assumptions.
The increasing intensity of extreme catastrophic events in recent years highlights the critical need for insurance to protect against their potential disastrous impacts. However, such catastrophic losses are often regarded as uninsurable by insurers, and there is a lack of risk-management solutions for them. Contrary to basic intuition, the literature has shown that within a specific class of risk-sharing rules, diversifying infinite-mean Pareto losses is always harmful. Consequently, the optimal action is non-diversification, which effectively leads to a lack of protection against such catastrophic risks. In this article, by considering a broader class of risk-sharing rules, we construct novel risk-sharing mechanisms as alternatives to non-diversification for managing catastrophic Pareto risks. To establish a foundation, we first study linear risk-sharing rules in a peer-to-peer risk-sharing setting with heterogeneity. Within this class, a Pareto optimal risk-sharing rule is obtained: uniform risk sharing among agents with finite-mean Pareto losses and no risk sharing among agents with infinite-mean Pareto losses. Next, by introducing nonlinearity, we construct two novel risk-sharing rules for managing infinite-mean catastrophic Pareto risks. We then present theoretical results to justify the benefits of the proposed risk-sharing rules, supported by numerical illustrations.
Grounded in network theory, this study examines how scholars' co-authorship networks influence their research performance and job mobility. The analysis of co-authorship networks of authors who published in the five leading risk, insurance, and actuarial journals from 2002 to 2020 indicates that an author's co-authorship network centrality-measured by the number of co-authors-positively correlates with her weighted numbers of publications and citations, whereas her co-authorship network cohesion-reflecting the strength and interconnectedness of relationships among co-authors-negatively correlates with these metrics. Additionally, increased cohesion within an author-school network (i.e., a collaborative network linking an author's institution to others) intensifies the impacts of co-authorship network centrality and cohesion on research performance. Lastly, our findings suggest that the probability of an author's job switch is positively correlated with her co-authorship network centrality and cohesion. These results underscore the significant role of co-authorship networks in shaping research outcomes and career trajectories, offering insights for authors considering collaboration and for universities and research institutions seeking to foster and support collaborative environments.
The aggregate loss distribution plays an important role in many actuarial applications, providing key insights into the risk profile of an insurance portfolio. Traditionally, a detailed assessment of this distribution relied either on various approximation methods or on recursive or convolution methods that necessitate the discretization of the loss distribution. In contrast to these approaches, this article introduces a mixture model for direct estimation of the aggregate loss distribution, where policyholders are grouped based on the number of claims they generate. The claim frequency distribution is explicitly accounted for within this model using the mixture weights, for example, based on a truncated Poisson distribution. Theoretical support for this mixture model is provided along with closed-form expressions for risk measures and the net stop-loss premium derived considering two severity distributions: gamma and lognormal. Furthermore, five existing approximation methods (normal, normal-power II, lognormal, gamma, and inverse Gaussian) are extended through the derivation of explicit formulas for risk measures and the net stop-loss premium. The proposed method is evaluated against these five approximation methods, as well as recursive and convolution methods, using both real-world data on French motor losses and simulation studies. The results indicate a suitable performance of the proposed approach, suggesting a potential shift away from traditional approximation and discretization-based methods.
This article examines how excess verdicts affect the insurance industry and studies insurance contract design from the policyholder's perspective, focusing on cases where court awards exceed policy limits. Excess verdicts refer to court decisions that grant compensation higher than the maximum coverage stated in an insurance policy. They are increasingly common in severe liability cases such as wrongful death claims and create both financial and legal risks for insurers and policyholders. These risks lead to uncertainty in premiums, solvency management, and overall risk control within the insurance market. To address these issues, we develop a mathematical framework that models excess verdicts by separating loss levels, legal outcomes, and contractual terms that specify coverage beyond standard policy limits. The framework applies value-at-risk (VaR) and conditional value-at-risk (CVaR) within a premium principle to capture the trade-off between risk exposure and cost in a manageable form. This approach provides a structured way to study how insurers and policyholders can share risks more efficiently when facing large and unpredictable legal awards. The results show that insurance contracts with multiple layers of indemnity can improve financial stability and fairness by distributing losses across different levels of coverage. Layered contracts reduce legal disputes, support balanced cost-sharing between insurers and policyholders, and give both sides clearer expectations about loss coverage. In practice, this structure helps insurers maintain solvency under extreme outcomes while offering policyholders more certainty about compensation in severe claim situations. The study provides a quantitative basis for designing more stable and transparent insurance products that can handle the growing problem of excess verdicts in modern markets.
We consider an insurance company that faces financial risk in the form of insurance claims and market-dependent surplus fluctuations. The company aims to simultaneously control its terminal wealth (e.g., at the end of an accounting period) and the ruin probability in a finite time interval by purchasing reinsurance. The target functional is given by the expected utility of terminal wealth perturbed by a modified Gerber-Shiu penalty function. We use neural networks to solve for the optimal reinsurance strategy and the corresponding maximal value of the target functional. The procedure is illustrated by a numerical example in which the surplus process is given by a Cram & eacute;r-Lundberg model perturbed by a mean-reverting Ornstein-Uhlenbeck process.
