Pub Date : 2025-08-13DOI: 10.1016/j.insmatheco.2025.103148
Dimitrios G. Konstantinides, Charalampos D. Passalidis
We study a multidimensional renewal risk model, with common counting process and càdlàg returns. Considering that the claim vectors have common distribution from some multivariate distribution class with heavy tail, are mutually weakly dependent, and each one has arbitrarily dependent components, we obtain uniformly asymptotic estimations for the probability of entrance of discounted aggregate claims into a some rare sets, over a finite time horizon. Direct consequence of the claim behavior is the estimation of the ruin probability of the model in some ruin sets. Further, restricting the distribution class of the claim vectors in the multivariate regular variation, the estimations still hold uniformly over the whole time horizon.
{"title":"Uniform asymptotic estimates for ruin probabilities of a multidimensional risk model with càdlàg returns and multivariate heavy tailed claims","authors":"Dimitrios G. Konstantinides, Charalampos D. Passalidis","doi":"10.1016/j.insmatheco.2025.103148","DOIUrl":"10.1016/j.insmatheco.2025.103148","url":null,"abstract":"<div><div>We study a multidimensional renewal risk model, with common counting process and càdlàg returns. Considering that the claim vectors have common distribution from some multivariate distribution class with heavy tail, are mutually weakly dependent, and each one has arbitrarily dependent components, we obtain uniformly asymptotic estimations for the probability of entrance of discounted aggregate claims into a some rare sets, over a finite time horizon. Direct consequence of the claim behavior is the estimation of the ruin probability of the model in some ruin sets. Further, restricting the distribution class of the claim vectors in the multivariate regular variation, the estimations still hold uniformly over the whole time horizon.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103148"},"PeriodicalIF":2.2,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144903671","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 : 2025-08-07DOI: 10.1016/j.insmatheco.2025.103140
Ling Wang , Bowen Jia
This paper investigates equilibrium investment strategies for a defined contribution (DC) pension plan member who faces random risk preferences. Downside protection for the pension plan and stochastic inflation are considered. The pension plan member is allowed to invest in cash, in an inflation-index bond, and in a stock in the financial market. Besides financial market risks, the wealth of the pension account is influenced by the stochastic contribution of the pension plan member. We adopt the framework proposed in Desmettre and Steffensen (2023) to tackle the time inconsistency issues arising from the incorporation of random risk aversion. The problem is first transformed into a self-financing investment problem and the semi-closed form of the equilibrium investment strategies is derived under the power utility function up to the solution of an ordinary differential equation (ODE) system. Our numerical analysis reveals that using expected risk aversion rather than random risk aversion results in a substantial welfare loss for the pension plan member.
{"title":"Equilibrium investment strategies for a defined contribution pension plan with random risk aversion","authors":"Ling Wang , Bowen Jia","doi":"10.1016/j.insmatheco.2025.103140","DOIUrl":"10.1016/j.insmatheco.2025.103140","url":null,"abstract":"<div><div>This paper investigates equilibrium investment strategies for a defined contribution (DC) pension plan member who faces random risk preferences. Downside protection for the pension plan and stochastic inflation are considered. The pension plan member is allowed to invest in cash, in an inflation-index bond, and in a stock in the financial market. Besides financial market risks, the wealth of the pension account is influenced by the stochastic contribution of the pension plan member. We adopt the framework proposed in <span><span>Desmettre and Steffensen (2023)</span></span> to tackle the time inconsistency issues arising from the incorporation of random risk aversion. The problem is first transformed into a self-financing investment problem and the semi-closed form of the equilibrium investment strategies is derived under the power utility function up to the solution of an ordinary differential equation (ODE) system. Our numerical analysis reveals that using expected risk aversion rather than random risk aversion results in a substantial welfare loss for the pension plan member.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103140"},"PeriodicalIF":2.2,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810533","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}
Risk budgeting is an effective risk management tool that a decision-maker uses to create a risk portfolio with a pre-determined risk profile. This paper provides a rich discussion about the theory and practice on how to construct risk budgeting portfolios in a variety of settings. We revisit the usual portfolio selection setting with and without clustered risk budgeting targets, and we then provide an approach on how to extend the usual setting to situations in which a non-hedgeable risk is present or fixed sub-portfolios are aimed by the decision-maker. Another study of this paper is how to include risk budgeting targets in risk sharing, which has not been discussed in the literature. Implementation issues are also discussed, and some bespoke algorithms are provided to identify such risk budgeting portfolios. Numerical experiments are performed for real-life financial data, and we explain the risk mitigation effect of our proposed portfolio. Specifically, financial risk budgeting portfolios with social responsibility targets are constructed.
{"title":"Portfolio selection and risk sharing via risk budgeting","authors":"Vali Asimit , Wing Fung Chong , Radu Tunaru , Feng Zhou","doi":"10.1016/j.insmatheco.2025.103139","DOIUrl":"10.1016/j.insmatheco.2025.103139","url":null,"abstract":"<div><div>Risk budgeting is an effective risk management tool that a decision-maker uses to create a risk portfolio with a pre-determined risk profile. This paper provides a rich discussion about the theory and practice on how to construct risk budgeting portfolios in a variety of settings. We revisit the usual portfolio selection setting with and without clustered risk budgeting targets, and we then provide an approach on how to extend the usual setting to situations in which a non-hedgeable risk is present or fixed sub-portfolios are aimed by the decision-maker. Another study of this paper is how to include risk budgeting targets in risk sharing, which has not been discussed in the literature. Implementation issues are also discussed, and some bespoke algorithms are provided to identify such risk budgeting portfolios. Numerical experiments are performed for real-life financial data, and we explain the risk mitigation effect of our proposed portfolio. Specifically, financial risk budgeting portfolios with social responsibility targets are constructed.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103139"},"PeriodicalIF":2.2,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144781829","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 : 2025-07-31DOI: 10.1016/j.insmatheco.2025.103133
Jingyi Cao , Dongchen Li , Virginia R. Young , Bin Zou
We develop and solve a two-layer game to model co-opetition, a strategic combination of competition and cooperation, in a reinsurance market consisting of one primary insurer and two reinsurers, in which all players are equipped with mean-variance preferences and the reinsurance contracts are priced under the variance premium principle. The insurer negotiates reinsurance contracts with the two reinsurers simultaneously, modeled by two Stackelberg games, and the two reinsurers compete for business from the same insurer by setting their own pricing rules, modeled by a non-cooperative Nash game. The combined Stackelberg-Nash game constitutes the first layer of the game model and endogenously determines the risk assumed by each reinsurer. The two reinsurers, then, participate in a cooperative risk-sharing game, forming the second layer of the game model, and seek Pareto-optimal risk-sharing rules. We obtain equilibrium strategies in closed form for both layers. The equilibrium of the Stackelberg-Nash game consists of two proportional reinsurance contracts, with the more risk-averse reinsurer assuming a smaller portion of the insurer's total risk. The Pareto-optimal risk-sharing rules further dictate that the more risk-averse reinsurer transfers a portion of its assumed risk to the less risk-averse reinsurer, at the cost of a positive side payment.
{"title":"Co-opetition in reinsurance markets: When Pareto meets Stackelberg and Nash","authors":"Jingyi Cao , Dongchen Li , Virginia R. Young , Bin Zou","doi":"10.1016/j.insmatheco.2025.103133","DOIUrl":"10.1016/j.insmatheco.2025.103133","url":null,"abstract":"<div><div>We develop and solve a two-layer game to model co-opetition, a strategic combination of competition and cooperation, in a reinsurance market consisting of one primary insurer and two reinsurers, in which all players are equipped with mean-variance preferences and the reinsurance contracts are priced under the variance premium principle. The insurer negotiates reinsurance contracts with the two reinsurers simultaneously, modeled by two Stackelberg games, and the two reinsurers compete for business from the same insurer by setting their own pricing rules, modeled by a non-cooperative Nash game. The combined Stackelberg-Nash game constitutes the first layer of the game model and endogenously determines the risk assumed by each reinsurer. The two reinsurers, then, participate in a cooperative risk-sharing game, forming the second layer of the game model, and seek Pareto-optimal risk-sharing rules. We obtain equilibrium strategies in closed form for both layers. The equilibrium of the Stackelberg-Nash game consists of two proportional reinsurance contracts, with the more risk-averse reinsurer assuming a smaller portion of the insurer's total risk. The Pareto-optimal risk-sharing rules further dictate that the more risk-averse reinsurer transfers a portion of its assumed risk to the less risk-averse reinsurer, at the cost of a positive side payment.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103133"},"PeriodicalIF":2.2,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144781830","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 : 2025-07-30DOI: 10.1016/j.insmatheco.2025.103136
Yaojun Zhang , Lanpeng Ji , Georgios Aivaliotis , Charles C. Taylor
This paper proposes three types of Bayesian CART (or BCART) models for aggregate claim amount, namely, frequency-severity models, sequential models and joint models. We propose a general framework for BCART models applicable to data with multivariate responses, which is particularly useful for the joint BCART models with a bivariate response: the number of claims and the aggregate claim amount. To facilitate frequency-severity modeling, we investigate BCART models for the right-skewed and heavy-tailed claim severity data using various distributions. We discover that the Weibull distribution is superior to gamma and lognormal distributions, due to its ability to capture different tail characteristics in tree models. Additionally, we find that sequential BCART models and joint BCART models, which can incorporate more complex dependence between the number of claims and severity, are beneficial and thus preferable to the frequency-severity BCART models in which independence is commonly assumed. The effectiveness of these models' performance is illustrated by carefully designed simulations and real insurance data.
{"title":"Bayesian CART models for aggregate claim modeling","authors":"Yaojun Zhang , Lanpeng Ji , Georgios Aivaliotis , Charles C. Taylor","doi":"10.1016/j.insmatheco.2025.103136","DOIUrl":"10.1016/j.insmatheco.2025.103136","url":null,"abstract":"<div><div>This paper proposes three types of Bayesian CART (or BCART) models for aggregate claim amount, namely, frequency-severity models, sequential models and joint models. We propose a general framework for BCART models applicable to data with multivariate responses, which is particularly useful for the joint BCART models with a bivariate response: the number of claims and the aggregate claim amount. To facilitate frequency-severity modeling, we investigate BCART models for the right-skewed and heavy-tailed claim severity data using various distributions. We discover that the Weibull distribution is superior to gamma and lognormal distributions, due to its ability to capture different tail characteristics in tree models. Additionally, we find that sequential BCART models and joint BCART models, which can incorporate more complex dependence between the number of claims and severity, are beneficial and thus preferable to the frequency-severity BCART models in which independence is commonly assumed. The effectiveness of these models' performance is illustrated by carefully designed simulations and real insurance data.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103136"},"PeriodicalIF":2.2,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144749841","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 : 2025-07-30DOI: 10.1016/j.insmatheco.2025.103135
Xi Xin , Giles Hooker , Fei Huang
The adoption of artificial intelligence (AI) across industries has led to the widespread use of complex black-box models and interpretation tools for decision making. This paper proposes an adversarial framework to uncover the vulnerability of permutation-based interpretation methods for machine learning tasks, with a particular focus on partial dependence (PD) plots. This adversarial framework modifies the original black box model to manipulate its predictions for instances in the extrapolation domain. As a result, it produces deceptive PD plots that can conceal discriminatory behaviors while preserving most of the original model's predictions. This framework can produce multiple fooled PD plots via a single model. By using real-world datasets including an auto insurance claims dataset and COMPAS (Correctional Offender Management Profiling for Alternative Sanctions) dataset, our results show that it is possible to intentionally hide the discriminatory behavior of a predictor and make the black-box model appear neutral through interpretation tools like PD plots while retaining almost all the predictions of the original black-box model. Managerial insights for regulators and practitioners are provided based on the findings.
{"title":"Pitfalls in machine learning interpretability: Manipulating partial dependence plots to hide discrimination","authors":"Xi Xin , Giles Hooker , Fei Huang","doi":"10.1016/j.insmatheco.2025.103135","DOIUrl":"10.1016/j.insmatheco.2025.103135","url":null,"abstract":"<div><div>The adoption of artificial intelligence (AI) across industries has led to the widespread use of complex black-box models and interpretation tools for decision making. This paper proposes an adversarial framework to uncover the vulnerability of permutation-based interpretation methods for machine learning tasks, with a particular focus on partial dependence (PD) plots. This adversarial framework modifies the original black box model to manipulate its predictions for instances in the extrapolation domain. As a result, it produces deceptive PD plots that can conceal discriminatory behaviors while preserving most of the original model's predictions. This framework can produce multiple fooled PD plots via a single model. By using real-world datasets including an auto insurance claims dataset and COMPAS (Correctional Offender Management Profiling for Alternative Sanctions) dataset, our results show that it is possible to intentionally hide the discriminatory behavior of a predictor and make the black-box model appear neutral through interpretation tools like PD plots while retaining almost all the predictions of the original black-box model. Managerial insights for regulators and practitioners are provided based on the findings.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"125 ","pages":"Article 103135"},"PeriodicalIF":2.2,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144749694","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 : 2025-07-07DOI: 10.1016/j.insmatheco.2025.103130
Takaaki Koike , Cathy W.S. Chen , Edward M.H. Lin
Capital allocation is a procedure for quantifying the contribution of each source of risk to aggregated risk. The gradient allocation rule, also known as the Euler principle, is a prevalent rule of capital allocation under which the allocated capital captures the diversification benefit of the marginal risk as a component of the overall risk. This paper concentrates on Expected Shortfall (ES) as a regulatory standard and focuses on the gradient allocations of ES, also called ES contributions (ESCs). We present the comprehensive treatment of backtesting the tuple of ESCs in the framework of the traditional and comparative backtests based on the concepts of joint identifiability and multi-objective elicitability. For robust forecast evaluation against the choice of scoring function, we also extend the Murphy diagram, a graphical tool to check whether one forecast dominates another under a class of scoring functions, to the case of ESCs. Finally, leveraging the recent concept of multi-objective elicitability, we propose a novel semiparametric model for forecasting dynamic ESCs based on a compositional regression model. In an empirical analysis of stock returns we evaluate and compare a variety of models for forecasting dynamic ESCs and demonstrate the solid performance of the proposed model.
{"title":"Forecasting and backtesting gradient allocations of expected shortfall","authors":"Takaaki Koike , Cathy W.S. Chen , Edward M.H. Lin","doi":"10.1016/j.insmatheco.2025.103130","DOIUrl":"10.1016/j.insmatheco.2025.103130","url":null,"abstract":"<div><div>Capital allocation is a procedure for quantifying the contribution of each source of risk to aggregated risk. The gradient allocation rule, also known as the Euler principle, is a prevalent rule of capital allocation under which the allocated capital captures the diversification benefit of the marginal risk as a component of the overall risk. This paper concentrates on Expected Shortfall (ES) as a regulatory standard and focuses on the gradient allocations of ES, also called ES contributions (ESCs). We present the comprehensive treatment of backtesting the tuple of ESCs in the framework of the traditional and comparative backtests based on the concepts of joint identifiability and multi-objective elicitability. For robust forecast evaluation against the choice of scoring function, we also extend the Murphy diagram, a graphical tool to check whether one forecast dominates another under a class of scoring functions, to the case of ESCs. Finally, leveraging the recent concept of multi-objective elicitability, we propose a novel semiparametric model for forecasting dynamic ESCs based on a compositional regression model. In an empirical analysis of stock returns we evaluate and compare a variety of models for forecasting dynamic ESCs and demonstrate the solid performance of the proposed model.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"124 ","pages":"Article 103130"},"PeriodicalIF":1.9,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144588381","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 : 2025-07-05DOI: 10.1016/j.insmatheco.2025.103131
Yuyu Chen , Paul Embrechts , Ruodu Wang
We study the optimal decisions and equilibria of agents who aim to minimize their risks by allocating their positions over extremely heavy-tailed (i.e., infinite-mean) and possibly dependent losses. The loss distributions of our focus are super-Pareto distributions, which include the class of extremely heavy-tailed Pareto distributions. Using a recent result on stochastic dominance, we show that for a portfolio of super-Pareto losses, non-diversification is preferred by decision makers equipped with well-defined and monotone risk measures. The phenomenon that diversification is not beneficial in the presence of super-Pareto losses is further illustrated by an equilibrium analysis in a risk exchange market. First, agents with super-Pareto losses will not share risks in a market equilibrium. Second, transferring losses from agents bearing super-Pareto losses to external parties without any losses may arrive at an equilibrium which benefits every party involved.
{"title":"Risk exchange under infinite-mean Pareto models","authors":"Yuyu Chen , Paul Embrechts , Ruodu Wang","doi":"10.1016/j.insmatheco.2025.103131","DOIUrl":"10.1016/j.insmatheco.2025.103131","url":null,"abstract":"<div><div>We study the optimal decisions and equilibria of agents who aim to minimize their risks by allocating their positions over extremely heavy-tailed (i.e., infinite-mean) and possibly dependent losses. The loss distributions of our focus are super-Pareto distributions, which include the class of extremely heavy-tailed Pareto distributions. Using a recent result on stochastic dominance, we show that for a portfolio of super-Pareto losses, non-diversification is preferred by decision makers equipped with well-defined and monotone risk measures. The phenomenon that diversification is not beneficial in the presence of super-Pareto losses is further illustrated by an equilibrium analysis in a risk exchange market. First, agents with super-Pareto losses will not share risks in a market equilibrium. Second, transferring losses from agents bearing super-Pareto losses to external parties without any losses may arrive at an equilibrium which benefits every party involved.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"124 ","pages":"Article 103131"},"PeriodicalIF":1.9,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144580825","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 : 2025-07-05DOI: 10.1016/j.insmatheco.2025.103132
Hong-Jie Li , Xing-Gang Luo , Zhong-Liang Zhang , Shen-Wei Huang , Wei Jiang
Usage-based insurance (UBI) charges drivers differently through telematics-based driving risk assessments. While current UBI pricing models differentiate driving risks, their overly discriminative prices may expel risky drivers, whose driving behaviors could have been modified, thereby incurring insurers' losses in profits. We propose a new UBI pricing model to address this problem by incorporating customer retention into the conventional UBI framework. Specifically, our model offers targeted discounts based on drivers' price sensitivity to retain those who may terminate the insurance contract, as well as provides concrete suggestions to help them modify unsafe driving behaviors. Using empirical data from a major Chinese auto insurer, we confirm that our model yields higher profits for insurers over the UBI pricing model that does not account for customer retention, and exemplify how suggestions for drivers can be drawn from driving profiles.
{"title":"A usage-based insurance (UBI) pricing model considering customer retention","authors":"Hong-Jie Li , Xing-Gang Luo , Zhong-Liang Zhang , Shen-Wei Huang , Wei Jiang","doi":"10.1016/j.insmatheco.2025.103132","DOIUrl":"10.1016/j.insmatheco.2025.103132","url":null,"abstract":"<div><div>Usage-based insurance (UBI) charges drivers differently through telematics-based driving risk assessments. While current UBI pricing models differentiate driving risks, their overly discriminative prices may expel risky drivers, whose driving behaviors could have been modified, thereby incurring insurers' losses in profits. We propose a new UBI pricing model to address this problem by incorporating customer retention into the conventional UBI framework. Specifically, our model offers targeted discounts based on drivers' price sensitivity to retain those who may terminate the insurance contract, as well as provides concrete suggestions to help them modify unsafe driving behaviors. Using empirical data from a major Chinese auto insurer, we confirm that our model yields higher profits for insurers over the UBI pricing model that does not account for customer retention, and exemplify how suggestions for drivers can be drawn from driving profiles.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"124 ","pages":"Article 103132"},"PeriodicalIF":1.9,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144580676","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 : 2025-06-25DOI: 10.1016/j.insmatheco.2025.103128
Melanie Averhoff, Julie Thøgersen
This paper provides a study of how experience rating on both claim frequency and severity impacts the solvency of an insurance business in the continuous-time Cramér Lundberg model. This is done by treating the claim parameters as random outcomes and continuously updating the premiums using Bayesian estimators. In the analysis, the claim sizes conditional on the severity parameter are assumed to be light-tailed. The main contributions are large deviation results where the asymptotic ruin probability is found for a model updating the premium based upon both frequency and severity. This asymptotic ruin probability is lower and decays faster compared to the one of a model which updates the premium solely based on claim frequency. Our findings are illustrated with examples, where the conditional claim size and the severity parameter are parametrised.
{"title":"Experience rating in the Cramér-Lundberg model","authors":"Melanie Averhoff, Julie Thøgersen","doi":"10.1016/j.insmatheco.2025.103128","DOIUrl":"10.1016/j.insmatheco.2025.103128","url":null,"abstract":"<div><div>This paper provides a study of how experience rating on both claim frequency and severity impacts the solvency of an insurance business in the continuous-time Cramér Lundberg model. This is done by treating the claim parameters as random outcomes and continuously updating the premiums using Bayesian estimators. In the analysis, the claim sizes conditional on the severity parameter are assumed to be light-tailed. The main contributions are large deviation results where the asymptotic ruin probability is found for a model updating the premium based upon both frequency and severity. This asymptotic ruin probability is lower and decays faster compared to the one of a model which updates the premium solely based on claim frequency. Our findings are illustrated with examples, where the conditional claim size and the severity parameter are parametrised.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"124 ","pages":"Article 103128"},"PeriodicalIF":1.9,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144518560","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}
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