模型不确定性下的最优消费策略

IF 1.3 Q2 STATISTICS & PROBABILITY

Statistics & Risk Modeling Pub Date : 2005-01-01 DOI:10.1524/stnd.2005.23.1.1

Christian Burgert, L. Rüschendorf

{"title":"模型不确定性下的最优消费策略","authors":"Christian Burgert, L. Rüschendorf","doi":"10.1524/stnd.2005.23.1.1","DOIUrl":null,"url":null,"abstract":"Summary In this paper we consider the problem of finding optimal consumption strategies in an incomplete semimartingale market model under model uncertainty. The quality of a consumption strategy is measured by not only one probability measure but as common in risk theory by a class of scenario measures. We formulate a dual version of the optimization problem and prove the existence of a saddle point and give a characterization of an optimal consumption strategy in terms of solutions of the dual problem. This generalizes results of Karatzas and Zitkovic (2003) for the optimal consumption problem under a fixed probability measure.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1524/stnd.2005.23.1.1","citationCount":"25","resultStr":"{\"title\":\"Optimal consumption strategies under model uncertainty\",\"authors\":\"Christian Burgert, L. Rüschendorf\",\"doi\":\"10.1524/stnd.2005.23.1.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Summary In this paper we consider the problem of finding optimal consumption strategies in an incomplete semimartingale market model under model uncertainty. The quality of a consumption strategy is measured by not only one probability measure but as common in risk theory by a class of scenario measures. We formulate a dual version of the optimization problem and prove the existence of a saddle point and give a characterization of an optimal consumption strategy in terms of solutions of the dual problem. This generalizes results of Karatzas and Zitkovic (2003) for the optimal consumption problem under a fixed probability measure.\",\"PeriodicalId\":44159,\"journal\":{\"name\":\"Statistics & Risk Modeling\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2005-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1524/stnd.2005.23.1.1\",\"citationCount\":\"25\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Statistics & Risk Modeling\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1524/stnd.2005.23.1.1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics & Risk Modeling","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1524/stnd.2005.23.1.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 25

摘要

本文研究了不完全半鞅市场模型在模型不确定性下的最优消费策略问题。消费策略的质量不仅由一种概率度量来衡量，而且在风险理论中通常由一类情景度量来衡量。我们提出了一个对偶版本的优化问题，证明了鞍点的存在性，并给出了对偶问题解的最优消费策略的表征。这推广了Karatzas和Zitkovic(2003)在固定概率测度下的最优消费问题的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Optimal consumption strategies under model uncertainty

Summary In this paper we consider the problem of finding optimal consumption strategies in an incomplete semimartingale market model under model uncertainty. The quality of a consumption strategy is measured by not only one probability measure but as common in risk theory by a class of scenario measures. We formulate a dual version of the optimization problem and prove the existence of a saddle point and give a characterization of an optimal consumption strategy in terms of solutions of the dual problem. This generalizes results of Karatzas and Zitkovic (2003) for the optimal consumption problem under a fixed probability measure.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Statistics & Risk Modeling STATISTICS & PROBABILITY-

CiteScore

1.80

自引率

6.70%

发文量

期刊介绍： Statistics & Risk Modeling (STRM) aims at covering modern methods of statistics and probabilistic modeling, and their applications to risk management in finance, insurance and related areas. The journal also welcomes articles related to nonparametric statistical methods and stochastic processes. Papers on innovative applications of statistical modeling and inference in risk management are also encouraged. Topics Statistical analysis for models in finance and insurance Credit-, market- and operational risk models Models for systemic risk Risk management Nonparametric statistical inference Statistical analysis of stochastic processes Stochastics in finance and insurance Decision making under uncertainty.