Reclassiffication risk is a major concern in health insurance where contracts are typically one year in length but health shocks often persist for much longer. While most health systems with private insurers pair short-run contracts with substantial pricing regulations to reduce reclassi_cation risk, long-term contracts with one-sided insurer commitment have significant potential to reduce reclassiffication risk without the negative side effects of price regulation, such as adverse selection. We theoretically characterize optimal long-term insurance contracts with one-sided commitment, extending the literature in directions necessary for studying health insurance markets. We leverage this characterization to provide a simple algorithm for computing optimal contracts from primitives. We estimate key market fundamentals using data on all under-65 privately insured consumers in Utah. We find that dynamic contracts are very effective at reducing reclassification risk for consumers who arrive to the market in good health, but they are ineffective for consumers who come to the market in bad health, demonstrating that there is a role for the government insurance of pre-market health risks. Individuals with steeply rising income profiles find front-loading costly, and thus relatively prefer ACA-type exchanges. Switching costs enhance, while myopia moderately compromises, the performance of dynamic contracts.
{"title":"Optimal Long-Term Health Insurance Contracts: Characterization, Computation, and Welfare Effects","authors":"Soheil Ghili, B. Handel, Igal Hendel, M. Whinston","doi":"10.2139/ssrn.3855055","DOIUrl":"https://doi.org/10.2139/ssrn.3855055","url":null,"abstract":"\u0000 Reclassiffication risk is a major concern in health insurance where contracts are typically one year in length but health shocks often persist for much longer. While most health systems with private insurers pair short-run contracts with substantial pricing regulations to reduce reclassi_cation risk, long-term contracts with one-sided insurer commitment have significant potential to reduce reclassiffication risk without the negative side effects of price regulation, such as adverse selection. We theoretically characterize optimal long-term insurance contracts with one-sided commitment, extending the literature in directions necessary for studying health insurance markets. We leverage this characterization to provide a simple algorithm for computing optimal contracts from primitives. We estimate key market fundamentals using data on all under-65 privately insured consumers in Utah. We find that dynamic contracts are very effective at reducing reclassification risk for consumers who arrive to the market in good health, but they are ineffective for consumers who come to the market in bad health, demonstrating that there is a role for the government insurance of pre-market health risks. Individuals with steeply rising income profiles find front-loading costly, and thus relatively prefer ACA-type exchanges. Switching costs enhance, while myopia moderately compromises, the performance of dynamic contracts.","PeriodicalId":111323,"journal":{"name":"DecisionSciRN: Insurance Risk Management (Sub-Topic)","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129072734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In insurance and even more in reinsurance it occurs that about a risk you only know that it has suffered no losses in the past e.g. seven years. Some of these risks are furthermore such particular or novel that there are no similar risks to infer the loss frequency from.
In this paper we propose a loss frequency estimator that copes with such situations, by just relying on the information coming from the risk itself: the “amended sample mean”. It is derived from a number of practice-oriented first principles and turns out to have desirable statistical properties.
Some variants are possible, which enables insurers to align the method to their preferred business strategy, by trading off between low initial premiums for new business and moderate premium increases for renewal business after a loss.
We further give examples where it is possible to assess the average loss from some market or portfolio information, such that overall one has an estimator of the risk premium.
{"title":"Premium Rating Without Losses: How To Estimate the Loss Frequency of Loss-Free Risks","authors":"Michael Fackler","doi":"10.2139/ssrn.3774382","DOIUrl":"https://doi.org/10.2139/ssrn.3774382","url":null,"abstract":"In insurance and even more in reinsurance it occurs that about a risk you only know that it has suffered no losses in the past e.g. seven years. Some of these risks are furthermore such particular or novel that there are no similar risks to infer the loss frequency from. <br><br>In this paper we propose a loss frequency estimator that copes with such situations, by just relying on the information coming from the risk itself: the “amended sample mean”. It is derived from a number of practice-oriented first principles and turns out to have desirable statistical properties. <br><br>Some variants are possible, which enables insurers to align the method to their preferred business strategy, by trading off between low initial premiums for new business and moderate premium increases for renewal business after a loss. <br><br>We further give examples where it is possible to assess the average loss from some market or portfolio information, such that overall one has an estimator of the risk premium.","PeriodicalId":111323,"journal":{"name":"DecisionSciRN: Insurance Risk Management (Sub-Topic)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115051428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper considers the robust equilibrium reinsurance and investment strategies for an ambiguity-averse insurer under a dynamic mean-variance criterion. The insurer is allowed to purchase excess-of-loss reinsurance and invest in a financial market consisting of a risk-free asset and a credit default swap (CDS). Following a game theoretic approach, robust equilibrium strategies and equilibrium value functions for the pre-default case and the post-default case are derived, respectively. For the ambiguity-averse insurer, in general the equilibrium strategies can be characterized by unique solutions to some algebraic equations. For the degenerate case with an ambiguity-neutral insurer, closed-form expressions of equilibrium strategies and equilibrium value functions are obtained. Moreover, we provide a simple condition under which the insurer should hold long/short positions in the CDS. Numerical examples demonstrate that the consideration of model uncertainty and CDS investment improves the insurer’s utility. In this regard, our paper establishes theoretical and numerical support for the importance of ambiguity aversion, credit risk and their interplay in insurance business.
{"title":"Robust Equilibrium Excess-of-Loss Reinsurance and CDS Investment Strategies for a Mean-Variance Insurer with Ambiguity Aversion","authors":"Hui Zhao, Yang Shen, Yan Zeng, Wenjun Zhang","doi":"10.2139/ssrn.3237442","DOIUrl":"https://doi.org/10.2139/ssrn.3237442","url":null,"abstract":"This paper considers the robust equilibrium reinsurance and investment strategies for an ambiguity-averse insurer under a dynamic mean-variance criterion. The insurer is allowed to purchase excess-of-loss reinsurance and invest in a financial market consisting of a risk-free asset and a credit default swap (CDS). Following a game theoretic approach, robust equilibrium strategies and equilibrium value functions for the pre-default case and the post-default case are derived, respectively. For the ambiguity-averse insurer, in general the equilibrium strategies can be characterized by unique solutions to some algebraic equations. For the degenerate case with an ambiguity-neutral insurer, closed-form expressions of equilibrium strategies and equilibrium value functions are obtained. Moreover, we provide a simple condition under which the insurer should hold long/short positions in the CDS. Numerical examples demonstrate that the consideration of model uncertainty and CDS investment improves the insurer’s utility. In this regard, our paper establishes theoretical and numerical support for the importance of ambiguity aversion, credit risk and their interplay in insurance business.","PeriodicalId":111323,"journal":{"name":"DecisionSciRN: Insurance Risk Management (Sub-Topic)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129651634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Carlos Vidal-Meliá, M. Ventura-Marco, Juan Manuel Pérez Salamero González
This paper develops a social insurance accounting model for a notional defined contribution (NDC) scheme combining retirement and long-term care (LTC) contingencies. The procedure relies on standard double-entry bookkeeping and enables us to compile a “Swedish” type actuarial balance sheet (ABS) following a framework equivalent to an open group approach. This methodology is suitable for reporting the system’s solvency status and can show periodical changes in the system’s financial position by means of an income statement. The information underpinning the actuarial valuation is based on events and transactions that are verifiable at the valuation date, without considering expected future trends. The paper also contains an illustrative example to make it easier for policymakers to understand the main advantages and difficulties of our proposal. The policy conclusions stress the need to properly report social insurance benefits to enhance transparency and sustainability and to improve decision-making because it is in the public interest to do so.
{"title":"A Social Insurance Accounting for a Notional Defined Contribution Scheme Combining Retirement and Long-Term Care Benefits","authors":"Carlos Vidal-Meliá, M. Ventura-Marco, Juan Manuel Pérez Salamero González","doi":"10.2139/ssrn.3235453","DOIUrl":"https://doi.org/10.2139/ssrn.3235453","url":null,"abstract":"This paper develops a social insurance accounting model for a notional defined contribution (NDC) scheme combining retirement and long-term care (LTC) contingencies. The procedure relies on standard double-entry bookkeeping and enables us to compile a “Swedish” type actuarial balance sheet (ABS) following a framework equivalent to an open group approach. This methodology is suitable for reporting the system’s solvency status and can show periodical changes in the system’s financial position by means of an income statement. The information underpinning the actuarial valuation is based on events and transactions that are verifiable at the valuation date, without considering expected future trends. The paper also contains an illustrative example to make it easier for policymakers to understand the main advantages and difficulties of our proposal. The policy conclusions stress the need to properly report social insurance benefits to enhance transparency and sustainability and to improve decision-making because it is in the public interest to do so.","PeriodicalId":111323,"journal":{"name":"DecisionSciRN: Insurance Risk Management (Sub-Topic)","volume":"269 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122948121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Natural catastrophes attract regularly the attention of media and have become a source of public concern. From a financial viewpoint, natural catastrophes represent idiosyncratic risks, diversifiable at the world level. But for reasons analyzed in this paper reinsurance markets are unable to cope with this risk completely. Insurance-linked securities, such as cat bonds, have been issued to complete the international risk transfer process, but their development is disappointing so far. This paper argues that downside risk aversion and ambiguity aversion explain the limited success of cat bonds. Hybrid cat bonds, combining the transfer of cat risk with protection against a stock market crash, are proposed to complete the market. Using the concept of market modified risk measure, the paper shows that replacing simple cat bonds with hybrid cat bonds would lead to an increase in market volume.
{"title":"Hybrid Cat-Bonds","authors":"P. Barrieu, Henri Loubergé","doi":"10.2139/ssrn.1016028","DOIUrl":"https://doi.org/10.2139/ssrn.1016028","url":null,"abstract":"Natural catastrophes attract regularly the attention of media and have become a source of public concern. From a financial viewpoint, natural catastrophes represent idiosyncratic risks, diversifiable at the world level. But for reasons analyzed in this paper reinsurance markets are unable to cope with this risk completely. Insurance-linked securities, such as cat bonds, have been issued to complete the international risk transfer process, but their development is disappointing so far. This paper argues that downside risk aversion and ambiguity aversion explain the limited success of cat bonds. Hybrid cat bonds, combining the transfer of cat risk with protection against a stock market crash, are proposed to complete the market. Using the concept of market modified risk measure, the paper shows that replacing simple cat bonds with hybrid cat bonds would lead to an increase in market volume.","PeriodicalId":111323,"journal":{"name":"DecisionSciRN: Insurance Risk Management (Sub-Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131213292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：