{"title":"Precautionary risk-reduction and saving decisions: Two sides of the same coin?","authors":"Richard Peter , Annette Hofmann","doi":"10.1016/j.insmatheco.2024.07.001","DOIUrl":null,"url":null,"abstract":"<div><p>We provide new results about the comparative static effects of income risk and interest rate risk on optimal risk-reduction and saving decisions. We combine arguments from the risk apportionment literature with monotone comparative statics. Risk reduction and saving are Edgeworth-Pareto substitutes for (mixed) risk averters and Edgeworth-Pareto complements for (mixed) risk lovers. For changes in income risk, risk reduction and saving are <em>N</em>th-degree risk complements for risk lovers. For changes in interest rate risk, risk reduction and saving are <em>N</em>th-degree risk substitutes for risk averters. The individual's risk attitude and the source of risk thus co-determine the effects of risk changes on optimal. We also discuss several extensions including multiple loss states, higher-order risk reduction, stochastic dominance, non-separable utility, and inflation risk.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":"118 ","pages":"Pages 175-194"},"PeriodicalIF":1.9000,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Insurance Mathematics & Economics","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167668724000787","RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
Abstract
We provide new results about the comparative static effects of income risk and interest rate risk on optimal risk-reduction and saving decisions. We combine arguments from the risk apportionment literature with monotone comparative statics. Risk reduction and saving are Edgeworth-Pareto substitutes for (mixed) risk averters and Edgeworth-Pareto complements for (mixed) risk lovers. For changes in income risk, risk reduction and saving are Nth-degree risk complements for risk lovers. For changes in interest rate risk, risk reduction and saving are Nth-degree risk substitutes for risk averters. The individual's risk attitude and the source of risk thus co-determine the effects of risk changes on optimal. We also discuss several extensions including multiple loss states, higher-order risk reduction, stochastic dominance, non-separable utility, and inflation risk.
我们提供了关于收入风险和利率风险对最优风险降低和储蓄决策的比较静态影响的新结果。我们将风险分摊文献的论点与单调比较静态相结合。对于（混合）风险规避者来说，降低风险和储蓄是埃奇沃思-帕雷托替代品，而对于（混合）风险爱好者来说，降低风险和储蓄是埃奇沃思-帕雷托互补品。对于风险爱好者来说，在收入风险发生变化时，减少风险和储蓄是 N 度风险互补。对于风险规避者来说，对于利率风险的变化来说，减少风险和储蓄是 N 度风险替代。因此，个人的风险态度和风险来源共同决定了风险变化对最优的影响。我们还讨论了一些扩展问题，包括多重损失状态、高阶风险降低、随机支配、不可分割效用和通货膨胀风险。
期刊介绍：
Insurance: Mathematics and Economics publishes leading research spanning all fields of actuarial science research. It appears six times per year and is the largest journal in actuarial science research around the world.
Insurance: Mathematics and Economics is an international academic journal that aims to strengthen the communication between individuals and groups who develop and apply research results in actuarial science. The journal feels a particular obligation to facilitate closer cooperation between those who conduct research in insurance mathematics and quantitative insurance economics, and practicing actuaries who are interested in the implementation of the results. To this purpose, Insurance: Mathematics and Economics publishes high-quality articles of broad international interest, concerned with either the theory of insurance mathematics and quantitative insurance economics or the inventive application of it, including empirical or experimental results. Articles that combine several of these aspects are particularly considered.
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