{"title":"用加权熵风险度量控制风险的最优投资","authors":"Jianming Xia","doi":"10.1137/22m152894x","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 54-92, March 2024. <br/> Abstract.A risk measure that is consistent with the second-order stochastic dominance and additive for sums of independent random variables can be represented as a weighted entropic risk measure (WERM). The expected utility maximization problem with risk controlled by WERM and a related risk minimization problem are investigated in this paper. The latter is equivalent to a problem of maximizing a weighted average of constant-absolute-risk-aversion certainty equivalents. The solutions of all the optimization problems are explicitly characterized, and an iterative method is provided to obtain the solutions numerically.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimal Investment with Risk Controlled by Weighted Entropic Risk Measures\",\"authors\":\"Jianming Xia\",\"doi\":\"10.1137/22m152894x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 54-92, March 2024. <br/> Abstract.A risk measure that is consistent with the second-order stochastic dominance and additive for sums of independent random variables can be represented as a weighted entropic risk measure (WERM). The expected utility maximization problem with risk controlled by WERM and a related risk minimization problem are investigated in this paper. The latter is equivalent to a problem of maximizing a weighted average of constant-absolute-risk-aversion certainty equivalents. The solutions of all the optimization problems are explicitly characterized, and an iterative method is provided to obtain the solutions numerically.\",\"PeriodicalId\":48880,\"journal\":{\"name\":\"SIAM Journal on Financial Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-02-27\",\"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/10.1137/22m152894x\",\"RegionNum\":4,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"BUSINESS, FINANCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Financial Mathematics","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1137/22m152894x","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
Optimal Investment with Risk Controlled by Weighted Entropic Risk Measures
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 54-92, March 2024. Abstract.A risk measure that is consistent with the second-order stochastic dominance and additive for sums of independent random variables can be represented as a weighted entropic risk measure (WERM). The expected utility maximization problem with risk controlled by WERM and a related risk minimization problem are investigated in this paper. The latter is equivalent to a problem of maximizing a weighted average of constant-absolute-risk-aversion certainty equivalents. The solutions of all the optimization problems are explicitly characterized, and an iterative method is provided to obtain the solutions numerically.
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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