具有两个风险因素的最优停止问题的一般框架及实物期权应用

IF 1.3 4区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Applied Stochastic Models in Business and Industry Pub Date : 2023-08-14 DOI:10.1002/asmb.2810

Rossella Agliardi

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引用次数: 0

摘要

给出了实物期权理论中一类广义二维最优停止问题的一个新的显式解。首先，在一个综合框架中给出了齐次和拟齐次问题的可解情况。然后考虑了一般问题——包括非齐次函数的未解决情况——并根据第二类修正贝塞尔函数得到了值函数的显式表达式。然后，我们阐明了在特定（拟）齐次问题中，通解方法和更初等的方法之间的联系。最后，本文还为一维情况提供了一些有用的公式和一些见解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A general framework for optimal stopping problems with two risk factors and real option applications

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.

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来源期刊

Applied Stochastic Models in Business and Industry 数学-数学跨学科应用

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

>12 weeks

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.