{"title":"泛函Ito公式在有界记忆随机投资组合优化中的应用","authors":"Tao Pang, Azmat Hussain","doi":"10.1137/1.9781611974072.23","DOIUrl":null,"url":null,"abstract":"We consider a stochastic portfolio optimization model in which the returns of risky asset depend on its past performance. The price of the risky asset is described by a stochastic delay differential equation. The investor’s goal is to maximize the expected discounted utility by choosing optimal investment and consumption as controls. We use the functional Ito’s formula to derive the associated HamiltonJacobi-Bellman equation. For logarithmic and exponential utility functions, we can obtain explicit solutions in a finite dimensional space.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"26","resultStr":"{\"title\":\"An Application of Functional Ito's Formula to Stochastic Portfolio Optimization with Bounded Memory\",\"authors\":\"Tao Pang, Azmat Hussain\",\"doi\":\"10.1137/1.9781611974072.23\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a stochastic portfolio optimization model in which the returns of risky asset depend on its past performance. The price of the risky asset is described by a stochastic delay differential equation. The investor’s goal is to maximize the expected discounted utility by choosing optimal investment and consumption as controls. We use the functional Ito’s formula to derive the associated HamiltonJacobi-Bellman equation. For logarithmic and exponential utility functions, we can obtain explicit solutions in a finite dimensional space.\",\"PeriodicalId\":193106,\"journal\":{\"name\":\"SIAM Conf. on Control and its Applications\",\"volume\":\"9 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"26\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Conf. on Control and its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/1.9781611974072.23\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Conf. on Control and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/1.9781611974072.23","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An Application of Functional Ito's Formula to Stochastic Portfolio Optimization with Bounded Memory
We consider a stochastic portfolio optimization model in which the returns of risky asset depend on its past performance. The price of the risky asset is described by a stochastic delay differential equation. The investor’s goal is to maximize the expected discounted utility by choosing optimal investment and consumption as controls. We use the functional Ito’s formula to derive the associated HamiltonJacobi-Bellman equation. For logarithmic and exponential utility functions, we can obtain explicit solutions in a finite dimensional space.
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