{"title":"A general framework for optimal stopping problems with two risk factors and real option applications","authors":"Rossella Agliardi","doi":"10.1002/asmb.2810","DOIUrl":null,"url":null,"abstract":"<p>A new explicit solution is obtained for a general class of two-dimensional optimal stopping problems arising in real option theory. First, the solvable case of homogeneous and quasi-homogeneous problems is presented in a comprehensive framework. Then the general problem—including the unsolved case of inhomogeneous functions—is considered and an explicit expression for the value function is obtained in terms of a modified Bessel function of second kind. Then we clarify the link between the general solution method and the more elementary one in the specific (quasi-)homogeneous problem. Finally, this article provides some useful formulas and some insights for the one-dimensional case as well.</p>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Stochastic Models in Business and Industry","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/asmb.2810","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
A new explicit solution is obtained for a general class of two-dimensional optimal stopping problems arising in real option theory. First, the solvable case of homogeneous and quasi-homogeneous problems is presented in a comprehensive framework. Then the general problem—including the unsolved case of inhomogeneous functions—is considered and an explicit expression for the value function is obtained in terms of a modified Bessel function of second kind. Then we clarify the link between the general solution method and the more elementary one in the specific (quasi-)homogeneous problem. Finally, this article provides some useful formulas and some insights for the one-dimensional case as well.
期刊介绍：
ASMBI - Applied Stochastic Models in Business and Industry (formerly Applied Stochastic Models and Data Analysis) was first published in 1985, publishing contributions in the interface between stochastic modelling, data analysis and their applications in business, finance, insurance, management and production. In 2007 ASMBI became the official journal of the International Society for Business and Industrial Statistics (www.isbis.org). The main objective is to publish papers, both technical and practical, presenting new results which solve real-life problems or have great potential in doing so. Mathematical rigour, innovative stochastic modelling and sound applications are the key ingredients of papers to be published, after a very selective review process.
The journal is very open to new ideas, like Data Science and Big Data stemming from problems in business and industry or uncertainty quantification in engineering, as well as more traditional ones, like reliability, quality control, design of experiments, managerial processes, supply chains and inventories, insurance, econometrics, financial modelling (provided the papers are related to real problems). The journal is interested also in papers addressing the effects of business and industrial decisions on the environment, healthcare, social life. State-of-the art computational methods are very welcome as well, when combined with sound applications and innovative models.
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