{"title":"Consumption-investment optimization with Epstein-Zin utility in unbounded non-Markovian markets","authors":"Zixin Feng, Dejian Tian, Harry Zheng","doi":"arxiv-2407.19995","DOIUrl":null,"url":null,"abstract":"The paper investigates the consumption-investment problem for an investor\nwith Epstein-Zin utility in an incomplete market. A non-Markovian environment\nwith unbounded parameters is considered, which is more realistic in practical\nfinancial scenarios compared to the Markovian setting. The optimal consumption\nand investment strategies are derived using the martingale optimal principle\nand quadratic backward stochastic differential equations (BSDEs) whose\nsolutions admit some exponential moment. This integrability property plays a\ncrucial role in establishing a key martingale argument. In addition, the paper\nalso examines the associated dual problem and several models within the\nspecified parameter framework.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"191 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Mathematical Finance","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.19995","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The paper investigates the consumption-investment problem for an investor
with Epstein-Zin utility in an incomplete market. A non-Markovian environment
with unbounded parameters is considered, which is more realistic in practical
financial scenarios compared to the Markovian setting. The optimal consumption
and investment strategies are derived using the martingale optimal principle
and quadratic backward stochastic differential equations (BSDEs) whose
solutions admit some exponential moment. This integrability property plays a
crucial role in establishing a key martingale argument. In addition, the paper
also examines the associated dual problem and several models within the
specified parameter framework.
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