{"title":"Existence and Computation of the Aumann-Serrano Index of Riskiness and Its Extension","authors":"K. Schulze","doi":"10.2139/ssrn.1156933","DOIUrl":null,"url":null,"abstract":"Aumann and Serrano (2008) introduce the index of riskiness to quantify the risk of a gamble. We discuss for which gambles this index of riskiness exists by considering the acceptance behavior of CARA-agents. Since for several relevant distributions riskiness is not defined, we suggest an extension of riskiness to all gambles. We prove that this extension is unique and that it satisfies the central duality axiom. Finally, we derive closed-form solutions of extended riskiness and list some applications.","PeriodicalId":46697,"journal":{"name":"Journal of Risk","volume":"1 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2013-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2139/ssrn.1156933","citationCount":"34","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Risk","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.2139/ssrn.1156933","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
引用次数: 34
Abstract
Aumann and Serrano (2008) introduce the index of riskiness to quantify the risk of a gamble. We discuss for which gambles this index of riskiness exists by considering the acceptance behavior of CARA-agents. Since for several relevant distributions riskiness is not defined, we suggest an extension of riskiness to all gambles. We prove that this extension is unique and that it satisfies the central duality axiom. Finally, we derive closed-form solutions of extended riskiness and list some applications.
期刊介绍：
This international peer-reviewed journal publishes a broad range of original research papers which aim to further develop understanding of financial risk management. As the only publication devoted exclusively to theoretical and empirical studies in financial risk management, The Journal of Risk promotes far-reaching research on the latest innovations in this field, with particular focus on the measurement, management and analysis of financial risk. The Journal of Risk is particularly interested in papers on the following topics: Risk management regulations and their implications, Risk capital allocation and risk budgeting, Efficient evaluation of risk measures under increasingly complex and realistic model assumptions, Impact of risk measurement on portfolio allocation, Theoretical development of alternative risk measures, Hedging (linear and non-linear) under alternative risk measures, Financial market model risk, Estimation of volatility and unanticipated jumps, Capital allocation.
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