{"title":"Fully Dynamic Risk Measures: Horizon Risk, Time-Consistency, and Relations with BSDEs and BSVIEs","authors":"Giulia Di Nunno, Emanuela Rosazza Gianin","doi":"10.1137/23m1546804","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Financial Mathematics, Volume 15, Issue 2, Page 399-435, June 2024. <br/> Abstract.In a dynamic framework, we identify a new concept associated with the risk of assessing the financial exposure by a measure that is not adequate to the actual time horizon of the position. This will be called horizon risk. We clarify that dynamic risk measures are subject to horizon risk, so we propose to use the fully dynamic version. To quantify horizon risk, we introduce h-longevity as an indicator. We investigate these notions together with other properties of risk measures, such as normalization, restriction property, and different formulations of time-consistency. We also consider these concepts for fully dynamic risk measures generated by backward stochastic differential equations (BSDEs), backward stochastic Volterra integral equations (BSVIEs), and families of these. Within this study, we provide new results for BSVIEs, such as a converse comparison theorem and the dual representation of the associated risk measures.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Financial Mathematics","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1137/23m1546804","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
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Abstract
SIAM Journal on Financial Mathematics, Volume 15, Issue 2, Page 399-435, June 2024. Abstract.In a dynamic framework, we identify a new concept associated with the risk of assessing the financial exposure by a measure that is not adequate to the actual time horizon of the position. This will be called horizon risk. We clarify that dynamic risk measures are subject to horizon risk, so we propose to use the fully dynamic version. To quantify horizon risk, we introduce h-longevity as an indicator. We investigate these notions together with other properties of risk measures, such as normalization, restriction property, and different formulations of time-consistency. We also consider these concepts for fully dynamic risk measures generated by backward stochastic differential equations (BSDEs), backward stochastic Volterra integral equations (BSVIEs), and families of these. Within this study, we provide new results for BSVIEs, such as a converse comparison theorem and the dual representation of the associated risk measures.
期刊介绍：
SIAM Journal on Financial Mathematics (SIFIN) addresses theoretical developments in financial mathematics as well as breakthroughs in the computational challenges they encompass. The journal provides a common platform for scholars interested in the mathematical theory of finance as well as practitioners interested in rigorous treatments of the scientific computational issues related to implementation. On the theoretical side, the journal publishes articles with demonstrable mathematical developments motivated by models of modern finance. On the computational side, it publishes articles introducing new methods and algorithms representing significant (as opposed to incremental) improvements on the existing state of affairs of modern numerical implementations of applied financial mathematics.
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