{"title":"A GREEDY ALGORITHM FOR HABIT FORMATION UNDER MULTIPLICATIVE UTILITY","authors":"SNEZHANA KIRUSHEVA, THOMAS S. SALISBURY","doi":"10.1142/s0219024923500279","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we consider the problem of optimizing lifetime consumption under a habit formation model, both with and without an exogenous pension. Unlike much of the existing literature, we apply a power utility to the ratio of consumption to habit, rather than to their difference. The martingale/duality method becomes intractable in this setting, so we develop a greedy version of this method that is solvable using Monte Carlo simulation. We investigate the behavior of the greedy solution, and explore what parameter values make the greedy solution a good approximation to the optimal one.</p>","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":"51 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Theoretical and Applied Finance","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0219024923500279","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
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Abstract
In this paper, we consider the problem of optimizing lifetime consumption under a habit formation model, both with and without an exogenous pension. Unlike much of the existing literature, we apply a power utility to the ratio of consumption to habit, rather than to their difference. The martingale/duality method becomes intractable in this setting, so we develop a greedy version of this method that is solvable using Monte Carlo simulation. We investigate the behavior of the greedy solution, and explore what parameter values make the greedy solution a good approximation to the optimal one.
期刊介绍：
The shift of the financial market towards the general use of advanced mathematical methods has led to the introduction of state-of-the-art quantitative tools into the world of finance. The International Journal of Theoretical and Applied Finance (IJTAF) brings together international experts involved in the mathematical modelling of financial instruments as well as the application of these models to global financial markets. The development of complex financial products has led to new challenges to the regulatory bodies. Financial instruments that have been designed to serve the needs of the mature capitals market need to be adapted for application in the emerging markets.
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