Insurance Mathematics & Economics最新文献

{"title":"Optimal reinsurance from an optimal transport perspective","authors":"Beatrice Acciaio ,&nbsp;Hansjörg Albrecher ,&nbsp;Brandon García Flores","doi":"10.1016/j.insmatheco.2025.03.004","DOIUrl":"10.1016/j.insmatheco.2025.03.004","url":null,"abstract":"<div><div>We use the randomization idea and proof techniques from optimal transport to study optimal reinsurance problems. We start by providing conditions for a class of problems that allow us to characterize the support of optimal treaties, and show how this can be used to deduce the shape of the optimal contract, reducing the task to an optimization problem with finitely many constraints, for which standard techniques can be applied. For a more general class of problems, we regard the optimal reinsurance problem as an iterated optimal transport problem between a (known) initial risk exposure of the insurer and an (unknown) resulting risk exposure of the reinsurer. The proposed approach provides a general framework that encompasses many reinsurance problems, which we illustrate in several concrete examples, providing alternative proofs to classical optimal reinsurance results, as well as establishing new optimality results, some of which contain optimal treaties that involve external randomness.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"122 ","pages":"Pages 194-213"},"PeriodicalIF":1.9,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143654758","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}

{"title":"A generalized tail mean-variance model for optimal capital allocation","authors":"Yang Yang ,&nbsp;Guojing Wang ,&nbsp;Jing Yao ,&nbsp;Hengyue Xie","doi":"10.1016/j.insmatheco.2025.03.003","DOIUrl":"10.1016/j.insmatheco.2025.03.003","url":null,"abstract":"<div><div>Capital allocation is a core task in financial and actuarial risk management. Some well-known capital allocation principles, such as the “Euler principle” and the “haircut principle”, have been widely used in the banking and insurance industry. The partitions of allocated capital not only serve as a buffer against potential losses but also provide certain risk pricing and performance measurement to the underlying risks. <span><span>Dhaene et al. (2012)</span></span> proposed a unified distance-minimizing capital allocation framework. Their objective function in the optimization only considers the magnitude of the loss function but not the variability. In this paper, we propose a general tail mean-variance (GTMV) model, which employs the Bregman divergences to construct distance-minimizing functions, and takes both the magnitude and the variability into account. We prove the existence and uniqueness of the optimal allocation and provide the general system of equations that characterizes the optimal solution. In this context, we further introduce the Mahalanobis tail mean-variance (MTMV) model and provide explicit distribution-free optimal allocation formulas, which cover many existing results as special cases. In particular, we derive the parametric analytical solutions for multivariate generalized hyperbolic distributed risks. For multivariate log-generalized hyperbolic distributed non-negative risks, we use the convex approximation method to obtain explicit solutions. We present two numerical examples showing the good performance of our optimal capital allocation rules. The first one analyzes the market risk of S&amp;P 500 industry sector indices. We show that our optimal capital allocation framework is applicable to various scenario analyses and provides a performance measure for the indices and the financial market. The other example is based on insurance claims from an Australian insurance company, showing our approximate formulas are both robust and accurate.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"122 ","pages":"Pages 157-179"},"PeriodicalIF":1.9,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577525","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}

{"title":"Pricing insurance contracts with an existing portfolio as background risk","authors":"Corrado De Vecchi ,&nbsp;Matthias Scherer","doi":"10.1016/j.insmatheco.2025.03.001","DOIUrl":"10.1016/j.insmatheco.2025.03.001","url":null,"abstract":"<div><div>We develop and investigate a premium principle that explicitly takes into account the impact of a new risk on some insurer's existing portfolio. Specifically, we propose the notion of an indifference premium for a new risk conditioned on an existing portfolio acting as background risk. The resulting premium rule, which in our case depends on the joint distribution of the new risk and the existing portfolio, is analyzed in detail with respect to its mathematical properties. In order to underline the differences between our approach and the literature on law-invariant premium rules, special attention is given to the indifference premium behaviour with respect to some well-known dependence concepts. Axiomatic and continuity properties of the proposed indifference premium rule are also investigated. To demonstrate the practical relevance of our approach, we consider a portfolio of exchangeable risks and investigate the role of the portfolio's dimension on the price of a risk to be added. This illustrates the (limits of) diversification benefits under the flexible exchangeability assumption on the joint distribution of a sequence of risks.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"122 ","pages":"Pages 180-193"},"PeriodicalIF":1.9,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577526","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}

{"title":"The impact of intermediaries on insurance demand and pricing","authors":"Dongchen Li ,&nbsp;Yan Zeng ,&nbsp;Yixing Zhao","doi":"10.1016/j.insmatheco.2025.03.002","DOIUrl":"10.1016/j.insmatheco.2025.03.002","url":null,"abstract":"<div><div>We study the impact of an independent insurance intermediary on insurance demand and pricing. The intermediary holds a fiduciary duty to an unsophisticated insurance buyer and adopts two remuneration systems: a fee-for-advice system and a commission system. Insurance contracting between the buyer (via the intermediary) and the insurer is formulated as a Stackelberg insurance game. Our analysis yields closed-form expressions for the buyer's equilibrium indemnity and the insurer's equilibrium premium loading. Subsequently, we explore the effects of fiduciary duty and remuneration arrangements on equilibrium strategies and stakeholder welfare, unraveling several economic implications. We find that the phenomenon of over-insuring at high premiums attributes to the deterioration of fiduciary duty. Additionally, our results point to the potential presence of tacit collusion between the intermediary and insurer. Moreover, we observe that there is no consensus among stakeholders regarding the most favored remuneration system in the market.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"122 ","pages":"Pages 143-156"},"PeriodicalIF":1.9,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143563598","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}

{"title":"Self-protection under Nth-degree risk increase of random unit cost","authors":"Yongjin Yin,&nbsp;Shengwang Meng","doi":"10.1016/j.insmatheco.2025.02.004","DOIUrl":"10.1016/j.insmatheco.2025.02.004","url":null,"abstract":"<div><div>Cost risk, as a type of multiplicative risk, should be given more attention in decision-making issues. Crainich and Menegatti (2021) have studied the effects of introducing random unit cost in self-protection under the four standard self-protection model frameworks. They focus on the case where the unit cost of effort in self-protection changes from certainty (<em>denoted as</em> <span><math><mi>c</mi></math></span>) to randomness (<em>denoted as</em> <span><math><mover><mi>c</mi><mo>˜</mo></mover></math></span>) with <span><math><mrow><mi>E</mi><mo>[</mo><mover><mi>c</mi><mo>˜</mo></mover><mo>]</mo><mo>=</mo><mi>c</mi></mrow></math></span>, which represents second-degree risk increase in Ekern (1980). In this paper, we generalize the concept of second-degree risk increase to <em>N</em>th-degree risk increase and provide sufficient conditions for increasing or decreasing effort in self-protection, which are closely related to the parity of the order of the risk change and decision-maker's higher-order risk attitudes. We use the multiplicative effect and apportionment effect to explain the decision-maker's preference conditions.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"122 ","pages":"Pages 137-142"},"PeriodicalIF":1.9,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143550226","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}

{"title":"Efficient evaluation of risk allocations","authors":"Christopher Blier-Wong ,&nbsp;Hélène Cossette ,&nbsp;Etienne Marceau","doi":"10.1016/j.insmatheco.2025.02.006","DOIUrl":"10.1016/j.insmatheco.2025.02.006","url":null,"abstract":"<div><div>Expectations of marginals conditional on the total risk of a portfolio are crucial in risk-sharing and allocation. However, computing these conditional expectations may be challenging, especially in critical cases where the marginal risks have compound distributions or when the risks are dependent. We introduce a generating function method to compute these conditional expectations. We provide efficient algorithms to compute the conditional expectations of marginals given the total risk for a portfolio of risks with lattice-type support. We show that the ordinary generating function of unconditional expected allocations is a function of the multivariate probability generating function of the portfolio. The generating function method allows us to develop recursive and transform-based techniques to compute the unconditional expected allocations. We illustrate our method to large-scale risk-sharing and risk allocation problems, including cases where the marginal risks have compound distributions, where the portfolio is composed of dependent risks, and where the risks have heavy tails, leading in some cases to computational gains of several orders of magnitude. Our approach is useful for risk-sharing in peer-to-peer insurance and risk allocation based on Euler's rule.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"122 ","pages":"Pages 119-136"},"PeriodicalIF":1.9,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143550225","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}

{"title":"Efficient and proper generalised linear models with power link functions","authors":"Vali Asimit ,&nbsp;Alexandru Badescu ,&nbsp;Ziwei Chen ,&nbsp;Feng Zhou","doi":"10.1016/j.insmatheco.2025.02.005","DOIUrl":"10.1016/j.insmatheco.2025.02.005","url":null,"abstract":"<div><div>The generalised linear model is a flexible predictive model for observational data that is widely used in practice as it extends linear regression models to non-Gaussian data. In this paper, we introduce the concept of a properly defined generalised linear model by requiring the conditional mean of the response variable to be properly mapped through the chosen link function and the log-likelihood function to be concave. We provide a comprehensive classification of proper generalised linear models for the Tweedie family and its popular subclasses under different link function specifications. Our main theoretical findings show that most Tweedie generalised linear models are not proper for canonical and log link functions, and identify a rich class of proper Tweedie generalised linear models with power link functions. We provide a novel interpretability methodology for power link functions that is mathematically sound and very simple, which could help the adoption of such a link function that has not been used much in practice for its lack of interpretability. Using self-concordant log-likelihoods and linearisation techniques, we provide novel algorithms for estimating several special cases of proper and not proper Tweedie generalised linear models with power link functions. The effectiveness of our methods is determined through an extensive numerical comparison of our estimates and those obtained using three built-in packages, <strong>MATLAB</strong> <em>fitglm</em>, <strong>R</strong> <em>glm</em>2 and <strong>Python</strong> <span><math><mi>sm</mi><mo>.</mo><mi>GLM</mi></math></span> libraries, which are all implemented based on the standard Iteratively Reweighted Least Squares method. Overall, we find that our algorithms consistently outperform these benchmarks in terms of both accuracy and efficiency, the largest improvements being documented for high-dimensional settings. This is concluded for both simulated data and real data, which shows that our optimisation-based GLM implementation is a good alternative to the standard Iteratively Reweighted Least Squares implementations available in well-known software.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"122 ","pages":"Pages 91-118"},"PeriodicalIF":1.9,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529121","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}

{"title":"Almost stochastic dominance: Magnitude constraints on risk aversion","authors":"Liqun Liu ,&nbsp;Jack Meyer","doi":"10.1016/j.insmatheco.2025.02.003","DOIUrl":"10.1016/j.insmatheco.2025.02.003","url":null,"abstract":"<div><div>Almost stochastic dominance (ASD) extends conventional first and second degree stochastic dominance by placing restrictions on the variability in the first and second derivatives of utility. Such restrictions increase the number of random variables for which a unanimous ranking of one over the other occurs. This paper advances an alternative approach to ASD in which the magnitude of absolute or relative risk aversion is constrained with both an upper bound and a lower bound. Using the results of Meyer (1977b), the paper provides cumulative distribution function (CDF) characterizations of these forms of ASD. Simple closed-form necessary and sufficient conditions for these ASD relations are determined for the special cases where the absolute or relative risk aversion is only bounded on one end or when the pair of random variables being compared have single-crossing CDFs. In addition, the relationship of the new ASD definitions to those in the literature is explored.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"122 ","pages":"Pages 82-90"},"PeriodicalIF":1.9,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509102","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}

{"title":"Insurance contract for electric vehicle charging stations: A Stackelberg game-theoretic approach","authors":"Yuanmin Jin ,&nbsp;Zhuo Jin ,&nbsp;Jiaqin Wei","doi":"10.1016/j.insmatheco.2025.02.002","DOIUrl":"10.1016/j.insmatheco.2025.02.002","url":null,"abstract":"<div><div>The development of electric vehicles has led to an expansion of Electric Vehicle Charging Stations (EVCSs). However, this expansion also brings about significant amount of risks, resulting in financial loss for EVCSs. To address this issue, this paper proposes an optimal insurance model based on a Stackelberg game between an insurer and a risk-averse EVCS operator. In the game, the insurer sets the insurance premium, and the EVCS operator decides on her charging price and ceded loss function. The paper explores the existence of the optimal solution of the game under the assumption of <em>n</em>-point distributed loss, and also characterizes the optimal solution if the loss follows two-point distribution. Finally, numerical examples are provided to demonstrate the effects of parameters on the optimal solution.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"122 ","pages":"Pages 61-81"},"PeriodicalIF":1.9,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143438179","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}

{"title":"Auto insurance fraud detection: Leveraging cost sensitive and insensitive algorithms for comprehensive analysis","authors":"Meryem Yankol Schalck","doi":"10.1016/j.insmatheco.2025.02.001","DOIUrl":"10.1016/j.insmatheco.2025.02.001","url":null,"abstract":"<div><div>As technology and the economy continue to grow, fraud has a significant negative impact on business and society, and insurance fraud remains an important issue, posing challenges in both detection and prevention. This article provides a direct cost-sensitive learning approaches on enhancing traditional motor insurance fraud detection by leveraging real-world data sets. In this approach, the results are obtained by using the information available at the opening of the claim, FNOL. The data set (FNOL) contains numerical, categorical, and textual variables. The results show that machine learning techniques perform better statistically and can also be more effective than standard approaches in reducing fraud-related costs. Extreme Gradient Boosting (XGB) outperforms both cost-sensitive and cost-insensitive approaches based on performance measures. Our study indicates that a cost-sensitive strategy delivers greater financial benefits than a cost-insensitive approach.</div></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"122 ","pages":"Pages 44-60"},"PeriodicalIF":1.9,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419301","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}