Pub Date : 2024-12-30DOI: 10.1016/j.insmatheco.2024.12.004
Vali Asimit , Zhongyi Yuan , Feng Zhou
Simple tail similarity measures are investigated in this paper so that the overarching tail similarity between two distributions is captured. We develop some theoretical results to support our novel measures, where the focus is on asymptotic approximations of our similarity measures for Fréchet-type tails. A simulation study is provided to validate the effectiveness of our proposed measures and demonstrate their great potential in capturing the intricate tail similarity. We conclude that our measure and the standard comparisons between the (first-order) extreme index estimates provide complementary information, and one should analyze them in tandem rather than in isolation. We also provide a simple rule of thumb, summarized as a sequential decision rule, for using the two sources of information to assess tail similarity.
{"title":"Tail similarity","authors":"Vali Asimit , Zhongyi Yuan , Feng Zhou","doi":"10.1016/j.insmatheco.2024.12.004","DOIUrl":"10.1016/j.insmatheco.2024.12.004","url":null,"abstract":"<div><div>Simple tail similarity measures are investigated in this paper so that the overarching tail similarity between two distributions is captured. We develop some theoretical results to support our novel measures, where the focus is on asymptotic approximations of our similarity measures for Fréchet-type tails. A simulation study is provided to validate the effectiveness of our proposed measures and demonstrate their great potential in capturing the intricate tail similarity. We conclude that our measure and the standard comparisons between the (first-order) extreme index estimates provide complementary information, and one should analyze them in tandem rather than in isolation. We also provide a simple rule of thumb, summarized as a sequential decision rule, for using the two sources of information to assess tail similarity.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"121 ","pages":"Pages 26-44"},"PeriodicalIF":1.9,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143144744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-10DOI: 10.1016/j.insmatheco.2024.11.010
Hansjörg Albrecher , Brandon Garcia Flores , Christian Hipp
We propose a new class of dividend payment strategies for which one can easily control an infinite-time-horizon ruin probability constraint for an insurance company. When the risk process evolves as a spectrally negative Lévy process, we investigate analytical properties of these strategies and propose two numerical methods for finding explicit expressions for the optimal parameters. Numerical experiments show that the performance of these strategies is outstanding and, in some cases, even comparable to the overall-unconstrained optimal dividend strategy to maximize expected aggregate discounted dividend payments, despite the ruin constraint.
{"title":"Dividend corridors and a ruin constraint","authors":"Hansjörg Albrecher , Brandon Garcia Flores , Christian Hipp","doi":"10.1016/j.insmatheco.2024.11.010","DOIUrl":"10.1016/j.insmatheco.2024.11.010","url":null,"abstract":"<div><div>We propose a new class of dividend payment strategies for which one can easily control an infinite-time-horizon ruin probability constraint for an insurance company. When the risk process evolves as a spectrally negative Lévy process, we investigate analytical properties of these strategies and propose two numerical methods for finding explicit expressions for the optimal parameters. Numerical experiments show that the performance of these strategies is outstanding and, in some cases, even comparable to the overall-unconstrained optimal dividend strategy to maximize expected aggregate discounted dividend payments, despite the ruin constraint.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"121 ","pages":"Pages 1-25"},"PeriodicalIF":1.9,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143144745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.insmatheco.2024.11.007
Aleksandr Shemendyuk , Joël Wagner
As many developed countries face the challenges of an aging population, the need to efficiently plan and finance long-term care (LTC) becomes increasingly important. Understanding the dynamics of care requirements and their associated costs is essential for sustainable healthcare systems. In this study, we employ a multi-state Markov model to analyze the transitions between care states of elderly individuals within institutional LTC in the canton of Geneva, Switzerland. Utilizing a comprehensive dataset of 21 494 elderly residents, we grouped care levels into four broader categories reflecting the range from quasi-autonomy to severe dependency. Our model considers fixed covariates at admission, such as demographic details, medical diagnoses, and levels of dependence, to forecast transitions and associated costs. The main results illustrate significant variations in care trajectories and LTC costs across different health profiles, notably influenced by gender and initial care state. Females generally require longer periods with less intensive care, while conditions like severe and nervous diseases show quicker progression to more intensive care and higher initial costs. These transitions and expected length of stay in each state directly impact LTC costs, highlighting the necessity of advanced strategies to manage the financial burden. Our findings offer insights that can be utilized to optimize LTC services in response to the specific needs of institutionalized elderly people. These findings can be applied to enhance healthcare planning, the preparedness of infrastructure, and the design of insurance products.
{"title":"Evolution of institutional long-term care costs based on health factors","authors":"Aleksandr Shemendyuk , Joël Wagner","doi":"10.1016/j.insmatheco.2024.11.007","DOIUrl":"10.1016/j.insmatheco.2024.11.007","url":null,"abstract":"<div><div>As many developed countries face the challenges of an aging population, the need to efficiently plan and finance long-term care (LTC) becomes increasingly important. Understanding the dynamics of care requirements and their associated costs is essential for sustainable healthcare systems. In this study, we employ a multi-state Markov model to analyze the transitions between care states of elderly individuals within institutional LTC in the canton of Geneva, Switzerland. Utilizing a comprehensive dataset of 21<!--> <!-->494 elderly residents, we grouped care levels into four broader categories reflecting the range from quasi-autonomy to severe dependency. Our model considers fixed covariates at admission, such as demographic details, medical diagnoses, and levels of dependence, to forecast transitions and associated costs. The main results illustrate significant variations in care trajectories and LTC costs across different health profiles, notably influenced by gender and initial care state. Females generally require longer periods with less intensive care, while conditions like severe and nervous diseases show quicker progression to more intensive care and higher initial costs. These transitions and expected length of stay in each state directly impact LTC costs, highlighting the necessity of advanced strategies to manage the financial burden. Our findings offer insights that can be utilized to optimize LTC services in response to the specific needs of institutionalized elderly people. These findings can be applied to enhance healthcare planning, the preparedness of infrastructure, and the design of insurance products.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"120 ","pages":"Pages 107-130"},"PeriodicalIF":1.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.insmatheco.2024.11.008
Yue Shi , Antonio Punzo , Håkon Otneim , Antonello Maruotti
We analyze the temporal structure of a novel insurance dataset about home insurance claims related to rainfall-induced damage in Norway and employ a hidden semi-Markov model (HSMM) to capture the non-Gaussian nature and temporal dynamics of these claims. By examining a broad range of candidate sojourn and emission distributions and assessing the goodness-of-fit and commonly used risk measures of the corresponding HSMM, we identify an appropriate model for effectively representing insurance losses caused by rainfall-related incidents. Our findings highlight the importance of considering the temporal aspects of weather-related insurance claims and demonstrate that the proposed HSMM adeptly captures this feature. Moreover, the model estimates reveal a concerning trend: the risks associated with heavy rain in the context of home insurance have exhibited an upward trajectory between 2004 and 2020, aligning with the evidence of a changing climate. This insight has significant implications for insurance companies, providing them with valuable information for accurate and robust modeling in the face of climate uncertainties. By shedding light on the evolving risks related to heavy rain and their impact on home insurance, our study offers essential insights for insurance companies to adapt their strategies and effectively manage these emerging challenges. It underscores the necessity of incorporating climate change considerations into insurance models and emphasizes the importance of continuously monitoring and reassessing risk levels associated with rainfall-induced damage. Ultimately, our research contributes to the broader understanding of climate risk in the insurance industry and supports the development of resilient and sustainable insurance practices.
{"title":"Hidden semi-Markov models for rainfall-related insurance claims","authors":"Yue Shi , Antonio Punzo , Håkon Otneim , Antonello Maruotti","doi":"10.1016/j.insmatheco.2024.11.008","DOIUrl":"10.1016/j.insmatheco.2024.11.008","url":null,"abstract":"<div><div>We analyze the temporal structure of a novel insurance dataset about home insurance claims related to rainfall-induced damage in Norway and employ a hidden semi-Markov model (HSMM) to capture the non-Gaussian nature and temporal dynamics of these claims. By examining a broad range of candidate sojourn and emission distributions and assessing the goodness-of-fit and commonly used risk measures of the corresponding HSMM, we identify an appropriate model for effectively representing insurance losses caused by rainfall-related incidents. Our findings highlight the importance of considering the temporal aspects of weather-related insurance claims and demonstrate that the proposed HSMM adeptly captures this feature. Moreover, the model estimates reveal a concerning trend: the risks associated with heavy rain in the context of home insurance have exhibited an upward trajectory between 2004 and 2020, aligning with the evidence of a changing climate. This insight has significant implications for insurance companies, providing them with valuable information for accurate and robust modeling in the face of climate uncertainties. By shedding light on the evolving risks related to heavy rain and their impact on home insurance, our study offers essential insights for insurance companies to adapt their strategies and effectively manage these emerging challenges. It underscores the necessity of incorporating climate change considerations into insurance models and emphasizes the importance of continuously monitoring and reassessing risk levels associated with rainfall-induced damage. Ultimately, our research contributes to the broader understanding of climate risk in the insurance industry and supports the development of resilient and sustainable insurance practices.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"120 ","pages":"Pages 91-106"},"PeriodicalIF":1.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-17DOI: 10.1016/j.insmatheco.2024.11.004
Jingyi Cao , Dongchen Li , Virginia R. Young , Bin Zou
We study a continuous-time, loss-reporting problem for an insured with full insurance under the mean-variance (MV) criterion. When a loss occurs, the insured faces two options: she can report it to the insurer for full reimbursement but will pay a higher premium rate; or she can hide it from the insurer by paying it herself and enjoy a lower premium rate. The insured follows a barrier strategy for loss reporting and seeks an optimal barrier to maximize her MV preferences over a random horizon. We show that this problem yields an optimal barrier that is not necessarily decreasing with respect to the insured's risk aversion, as intuition suggests it should. To address this non-monotonicity, we propose two solutions: in the first solution, we restrict the feasible strategies to a bounded interval; in the second, we modify the MV criterion by replacing the variance of the insured's wealth with the variance of the insured's retained losses. We obtain the optimal barrier strategy in semiclosed form—as a unique positive zero of a nonlinear function—for both modified models, and we show that it is a decreasing function of the insured's risk aversion, as expected.
{"title":"Continuous-time optimal reporting with full insurance under the mean-variance criterion","authors":"Jingyi Cao , Dongchen Li , Virginia R. Young , Bin Zou","doi":"10.1016/j.insmatheco.2024.11.004","DOIUrl":"10.1016/j.insmatheco.2024.11.004","url":null,"abstract":"<div><div>We study a continuous-time, loss-reporting problem for an insured with full insurance under the mean-variance (MV) criterion. When a loss occurs, the insured faces two options: she can report it to the insurer for full reimbursement but will pay a higher premium rate; or she can hide it from the insurer by paying it herself and enjoy a lower premium rate. The insured follows a barrier strategy for loss reporting and seeks an optimal barrier to maximize her MV preferences over a random horizon. We show that this problem yields an optimal barrier that is not necessarily decreasing with respect to the insured's risk aversion, as intuition suggests it should. To address this non-monotonicity, we propose two solutions: in the first solution, we restrict the feasible strategies to a bounded interval; in the second, we modify the MV criterion by replacing the variance of the insured's wealth with the variance of the insured's retained losses. We obtain the optimal barrier strategy in semiclosed form—as a unique positive zero of a nonlinear function—for both modified models, and we show that it is a decreasing function of the insured's risk aversion, as expected.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"120 ","pages":"Pages 79-90"},"PeriodicalIF":1.9,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-15DOI: 10.1016/j.insmatheco.2024.11.002
Yang Feng , Tak Kuen Siu , Jinxia Zhu
Model uncertainty and ambiguity aversion have important consequences for decision-making under uncertainty in diverse fields such as insurance, finance and economics. Although model uncertainty has been considered in decision-making problems in finance and economics, as well as problems relevant to (re)-insurance, relatively little attention has been given to exploring implications of model uncertainty and ambiguity aversion for the optimal policies governing cash retention and dividend payout. On the other hand, taxes and transaction costs/fees have a significant impact on retained earnings and dividend strategies. Despite its technically challenging, their impacts on optimal dividend strategies have been studied in the literature. However, consequences of model uncertainty and ambiguity aversion for optimal dividend payout policies and related decision-making issues in the presence of transaction costs/taxes have not been well-understood. This paper aims to explore this relatively unknown zone and to articulate this technically challenging problem. Specifically, we shall provide a rigorous approach to examine the impacts of model uncertainty and ambiguity aversion on optimal cash retention and dividend payout strategies with fixed and proportional transaction costs/taxes. Our key findings include (1) model uncertainty and ambiguity aversion change the qualitative behaviour of optimal strategies. Say the optimal strategy is a multi-level lump-sum strategy and tends to have more levels than that of the problem without capturing model uncertainty (2) the value function tends to be rougher (in terms of smoothness) than that of the problem without incorporating model uncertainty.
{"title":"How might model uncertainty and transaction costs impact retained earning & dividend strategies? An examination through a classical insurance risk model","authors":"Yang Feng , Tak Kuen Siu , Jinxia Zhu","doi":"10.1016/j.insmatheco.2024.11.002","DOIUrl":"10.1016/j.insmatheco.2024.11.002","url":null,"abstract":"<div><div>Model uncertainty and ambiguity aversion have important consequences for decision-making under uncertainty in diverse fields such as insurance, finance and economics. Although model uncertainty has been considered in decision-making problems in finance and economics, as well as problems relevant to (re)-insurance, relatively little attention has been given to exploring implications of model uncertainty and ambiguity aversion for the optimal policies governing cash retention and dividend payout. On the other hand, taxes and transaction costs/fees have a significant impact on retained earnings and dividend strategies. Despite its technically challenging, their impacts on optimal dividend strategies have been studied in the literature. However, consequences of model uncertainty and ambiguity aversion for optimal dividend payout policies and related decision-making issues in the presence of transaction costs/taxes have not been well-understood. This paper aims to explore this relatively unknown zone and to articulate this technically challenging problem. Specifically, we shall provide a rigorous approach to examine the impacts of model uncertainty and ambiguity aversion on optimal cash retention and dividend payout strategies with fixed and proportional transaction costs/taxes. Our key findings include (1) model uncertainty and ambiguity aversion change the qualitative behaviour of optimal strategies. Say the optimal strategy is a multi-level lump-sum strategy and tends to have more levels than that of the problem without capturing model uncertainty (2) the value function tends to be rougher (in terms of smoothness) than that of the problem without incorporating model uncertainty.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"120 ","pages":"Pages 131-158"},"PeriodicalIF":1.9,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-15DOI: 10.1016/j.insmatheco.2024.11.005
Marcelo Brutti Righi, Fernanda Maria Müller, Marlon Ruoso Moresco
We propose a risk measurement approach for a risk-averse stochastic problem. We provide results that guarantee the existence of a solution to our problem. We characterize and explore the properties of the argmin as a risk measure and the minimum as a generalized deviation measure. We provide an example to demonstrate a specific application of our approach. Additionally, we present a numerical example of the problem's solution to illustrate the usefulness of our approach in risk management analysis.
{"title":"A risk measurement approach from risk-averse stochastic optimization of score functions","authors":"Marcelo Brutti Righi, Fernanda Maria Müller, Marlon Ruoso Moresco","doi":"10.1016/j.insmatheco.2024.11.005","DOIUrl":"10.1016/j.insmatheco.2024.11.005","url":null,"abstract":"<div><div>We propose a risk measurement approach for a risk-averse stochastic problem. We provide results that guarantee the existence of a solution to our problem. We characterize and explore the properties of the argmin as a risk measure and the minimum as a generalized deviation measure. We provide an example to demonstrate a specific application of our approach. Additionally, we present a numerical example of the problem's solution to illustrate the usefulness of our approach in risk management analysis.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"120 ","pages":"Pages 42-50"},"PeriodicalIF":1.9,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142662504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-14DOI: 10.1016/j.insmatheco.2024.11.003
Tim J. Boonen , Wenjun Jiang
This paper studies the optimal insurance contracting from the perspective of a decision maker (DM) who has an ambiguous understanding of the loss distribution. The ambiguity set of loss distributions is represented as a p-Wasserstein ball, with , centered around a specific benchmark distribution. The DM selects the indemnity function that minimizes the worst-case risk within the risk-minimization framework, considering the constraints of the Wasserstein ball. Assuming that the DM is endowed with a convex distortion risk measure and that insurance pricing follows the expected-value premium principle, we derive the explicit structures of both the indemnity function and the worst-case distribution using a novel survival-function-based representation of the Wasserstein distance. We examine a specific example where the DM employs the GlueVaR and provide numerical results to demonstrate the sensitivity of the worst-case distribution concerning the model parameters.
{"title":"Distributionally robust insurance under the Wasserstein distance","authors":"Tim J. Boonen , Wenjun Jiang","doi":"10.1016/j.insmatheco.2024.11.003","DOIUrl":"10.1016/j.insmatheco.2024.11.003","url":null,"abstract":"<div><div>This paper studies the optimal insurance contracting from the perspective of a decision maker (DM) who has an ambiguous understanding of the loss distribution. The ambiguity set of loss distributions is represented as a <em>p</em>-Wasserstein ball, with <span><math><mi>p</mi><mo>∈</mo><msup><mrow><mi>Z</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>, centered around a specific benchmark distribution. The DM selects the indemnity function that minimizes the worst-case risk within the risk-minimization framework, considering the constraints of the Wasserstein ball. Assuming that the DM is endowed with a convex distortion risk measure and that insurance pricing follows the expected-value premium principle, we derive the explicit structures of both the indemnity function and the worst-case distribution using a novel survival-function-based representation of the Wasserstein distance. We examine a specific example where the DM employs the GlueVaR and provide numerical results to demonstrate the sensitivity of the worst-case distribution concerning the model parameters.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"120 ","pages":"Pages 61-78"},"PeriodicalIF":1.9,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-13DOI: 10.1016/j.insmatheco.2024.11.006
Ning Ding , Xiao Ruan , Hao Wang , Yuan Liu
Automobile insurance fraud has become a critical concern for the insurance industry, posing significant threats to socio-economic stability and commercial interests. To tackle these challenges, this paper proposes a PSO-XGBoost fraud detection framework and uses explainable artificial intelligence to interpret the predictions. The framework combines an XGBoost classifier with the particle swarm optimization algorithm and is validated through a comparative evaluation against other models. Traditional methods, including SVM, Naive Bayes, Logistic Regression, and BP Neural Network, demonstrate moderate accuracy, ranging from 54.1% to 68.6%, while more advanced models like Random Forest reach up to 78.4%. Compared to the standard XGBoost, the PSO-optimized model achieves 3% superior accuracy, achieving an impressive 95% success rate. Moreover, SHAP is used to extract and visually depict the contribution of each feature to the model's predictions. It turns out that the policyholder's claim amount is the most significant factor in detecting automobile insurance fraud, with other factors such as vehicle type, responsible party, and the insurer's age also considerably influencing the prediction performance. This paper therefore proves that combining the PSO-XGBoost model with SHAP approach can substantially improve the early warning and prevention of automobile insurance fraud.
{"title":"Automobile Insurance Fraud Detection Based on PSO-XGBoost Model and Interpretable Machine Learning Method","authors":"Ning Ding , Xiao Ruan , Hao Wang , Yuan Liu","doi":"10.1016/j.insmatheco.2024.11.006","DOIUrl":"10.1016/j.insmatheco.2024.11.006","url":null,"abstract":"<div><div>Automobile insurance fraud has become a critical concern for the insurance industry, posing significant threats to socio-economic stability and commercial interests. To tackle these challenges, this paper proposes a PSO-XGBoost fraud detection framework and uses explainable artificial intelligence to interpret the predictions. The framework combines an XGBoost classifier with the particle swarm optimization algorithm and is validated through a comparative evaluation against other models. Traditional methods, including SVM, Naive Bayes, Logistic Regression, and BP Neural Network, demonstrate moderate accuracy, ranging from 54.1% to 68.6%, while more advanced models like Random Forest reach up to 78.4%. Compared to the standard XGBoost, the PSO-optimized model achieves 3% superior accuracy, achieving an impressive 95% success rate. Moreover, SHAP is used to extract and visually depict the contribution of each feature to the model's predictions. It turns out that the policyholder's claim amount is the most significant factor in detecting automobile insurance fraud, with other factors such as vehicle type, responsible party, and the insurer's age also considerably influencing the prediction performance. This paper therefore proves that combining the PSO-XGBoost model with SHAP approach can substantially improve the early warning and prevention of automobile insurance fraud.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"120 ","pages":"Pages 51-60"},"PeriodicalIF":1.9,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-12DOI: 10.1016/j.insmatheco.2024.11.001
Michel Denuit , Jan Dhaene , Mario Ghossoub , Christian Y. Robert
Two by-now folkloric results in the theory of risk sharing are that (i) any feasible allocation is convex-order-dominated by a comonotonic allocation; and (ii) an allocation is Pareto optimal for the convex order if and only if it is comonotonic. Here, comonotonicity corresponds to the so-called no-sabotage condition, which aligns the interests of all parties involved. Several proofs of these two results have been provided in the literature, all based on a version of the comonotonic improvement algorithm of Landsberger and Meilijson (1994) and a limit argument based on the Martingale Convergence Theorem. However, no proof of (i) is explicit enough to allow for an easy algorithmic implementation in practice; and no proof of (ii) provides a closed-form characterization of Pareto optima. In addition, while all of the existing proofs of (i) are provided only for the case of a two-agent economy with the observation that they can be easily extended beyond two agents, such an extension is far from being trivial in the context of the algorithm of Landsberger and Meilijson (1994) and it has never been explicitly implemented. In this paper, we provide novel proofs of these foundational results. Our proof of (i) is based on the theory of majorization and an extension of a result of Lorentz and Shimogaki (1968), which allows us to provide an explicit algorithmic construction that can be easily implemented beyond the case of two agents. In addition, our proof of (ii) leads to a crisp closed-form characterization of Pareto-optimal allocations in terms of α-quantiles (mixed quantiles). An application to peer-to-peer insurance, or collaborative insurance, illustrates the relevance of these results.
{"title":"Comonotonicity and Pareto optimality, with application to collaborative insurance","authors":"Michel Denuit , Jan Dhaene , Mario Ghossoub , Christian Y. Robert","doi":"10.1016/j.insmatheco.2024.11.001","DOIUrl":"10.1016/j.insmatheco.2024.11.001","url":null,"abstract":"<div><div>Two by-now folkloric results in the theory of risk sharing are that (i) any feasible allocation is convex-order-dominated by a comonotonic allocation; and (ii) an allocation is Pareto optimal for the convex order if and only if it is comonotonic. Here, comonotonicity corresponds to the so-called <em>no-sabotage condition</em>, which aligns the interests of all parties involved. Several proofs of these two results have been provided in the literature, all based on a version of the comonotonic improvement algorithm of <span><span>Landsberger and Meilijson (1994)</span></span> and a limit argument based on the Martingale Convergence Theorem. However, no proof of (i) is explicit enough to allow for an easy algorithmic implementation in practice; and no proof of (ii) provides a closed-form characterization of Pareto optima. In addition, while all of the existing proofs of (i) are provided only for the case of a two-agent economy with the observation that they can be easily extended beyond two agents, such an extension is far from being trivial in the context of the algorithm of <span><span>Landsberger and Meilijson (1994)</span></span> and it has never been explicitly implemented. In this paper, we provide novel proofs of these foundational results. Our proof of (i) is based on the theory of majorization and an extension of a result of <span><span>Lorentz and Shimogaki (1968)</span></span>, which allows us to provide an explicit algorithmic construction that can be easily implemented beyond the case of two agents. In addition, our proof of (ii) leads to a crisp closed-form characterization of Pareto-optimal allocations in terms of <em>α</em>-quantiles (mixed quantiles). An application to peer-to-peer insurance, or collaborative insurance, illustrates the relevance of these results.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"120 ","pages":"Pages 1-16"},"PeriodicalIF":1.9,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142662502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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