{"title":"Stability of the Epstein–Zin problem","authors":"Michael Monoyios, Oleksii Mostovyi","doi":"10.1111/mafi.12434","DOIUrl":null,"url":null,"abstract":"<p>We investigate the stability of the Epstein–Zin problem with respect to small distortions in the dynamics of the traded securities. We work in incomplete market model settings, where our parametrization of perturbations allows for joint distortions in returns and volatility of the risky assets and the interest rate. Considering empirically the most relevant specifications of risk aversion and elasticity of intertemporal substitution, we provide a condition that guarantees the convexity of the domain of the underlying problem and results in the existence and uniqueness of a solution to it. Then, we prove the convergence of the optimal consumption streams, the associated wealth processes, the indirect utility processes, and the value functions in the limit when the model perturbations vanish.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Finance","FirstCategoryId":"96","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/mafi.12434","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate the stability of the Epstein–Zin problem with respect to small distortions in the dynamics of the traded securities. We work in incomplete market model settings, where our parametrization of perturbations allows for joint distortions in returns and volatility of the risky assets and the interest rate. Considering empirically the most relevant specifications of risk aversion and elasticity of intertemporal substitution, we provide a condition that guarantees the convexity of the domain of the underlying problem and results in the existence and uniqueness of a solution to it. Then, we prove the convergence of the optimal consumption streams, the associated wealth processes, the indirect utility processes, and the value functions in the limit when the model perturbations vanish.
期刊介绍：
Mathematical Finance seeks to publish original research articles focused on the development and application of novel mathematical and statistical methods for the analysis of financial problems.
The journal welcomes contributions on new statistical methods for the analysis of financial problems. Empirical results will be appropriate to the extent that they illustrate a statistical technique, validate a model or provide insight into a financial problem. Papers whose main contribution rests on empirical results derived with standard approaches will not be considered.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
