A Stochastic Differential Equation Driven by Poisson Random Measure and Its Application in a Duopoly Market
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-04-21
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
We investigate a stochastic differential equation driven by Poisson random measure and its application in a duopoly market for a finite number of consumers with two unknown preferences.
The scopes of pricing for two monopolistic vendors are illustrated when the prices of items are determined by the number of buyers in the market.
The quantity of buyers is proved to obey a stochastic differential equation (SDE) driven by Poisson random measure which exists a unique solution.
We derive the Hamilton-Jacobi-Bellman (HJB) about vendors’ profits and provide a verification theorem about the problem.
When all consumers believe a vendor’s guidance about their preferences, the conditions that the other vendor’s profit is zero are obtained.
We give an example of this problem and acquire approximate solutions about the profits of the two vendors.
American Psychological Association (APA)
Wang, Tong& Liang, Hao. 2020. A Stochastic Differential Equation Driven by Poisson Random Measure and Its Application in a Duopoly Market. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-12.
https://search.emarefa.net/detail/BIM-1194332
Modern Language Association (MLA)
Wang, Tong& Liang, Hao. A Stochastic Differential Equation Driven by Poisson Random Measure and Its Application in a Duopoly Market. Mathematical Problems in Engineering No. 2020 (2020), pp.1-12.
https://search.emarefa.net/detail/BIM-1194332
American Medical Association (AMA)
Wang, Tong& Liang, Hao. A Stochastic Differential Equation Driven by Poisson Random Measure and Its Application in a Duopoly Market. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-12.
https://search.emarefa.net/detail/BIM-1194332
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1194332