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Optimal Reinsurance-Investment Problem under a CEV Model: Stochastic Differential Game Formulation
Joint Authors
Li, Cunfang
Li, Danping
Chen, Ruiqing
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-04-21
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
This paper focuses on a stochastic differential game played between two insurance companies, a big one and a small one.
In our model, the basic claim process is assumed to follow a Brownian motion with drift.
Both of two insurance companies purchase the reinsurance, respectively.
The big company has sufficient asset to invest in the risky asset which is described by the constant elasticity of variance (CEV) model and acquire new business like acting as a reinsurance company of other insurance companies, while the small company can invest in the risk-free asset and purchase reinsurance.
The game studied here is zero-sum where there is a single exponential utility.
The big company is trying to maximize the expected exponential utility of the terminal wealth to keep its advantage on surplus while simultaneously the small company is trying to minimize the same quantity to reduce its disadvantage.
In this paper, we describe the Nash equilibrium of the game and prove a verification theorem for the exponential utility.
By solving the corresponding Fleming-Bellman-Isaacs equations, we derive the optimal reinsurance and investment strategies.
Furthermore, numerical examples are presented to show our results.
American Psychological Association (APA)
Li, Danping& Chen, Ruiqing& Li, Cunfang. 2020. Optimal Reinsurance-Investment Problem under a CEV Model: Stochastic Differential Game Formulation. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-19.
https://search.emarefa.net/detail/BIM-1197826
Modern Language Association (MLA)
Li, Danping…[et al.]. Optimal Reinsurance-Investment Problem under a CEV Model: Stochastic Differential Game Formulation. Mathematical Problems in Engineering No. 2020 (2020), pp.1-19.
https://search.emarefa.net/detail/BIM-1197826
American Medical Association (AMA)
Li, Danping& Chen, Ruiqing& Li, Cunfang. Optimal Reinsurance-Investment Problem under a CEV Model: Stochastic Differential Game Formulation. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-19.
https://search.emarefa.net/detail/BIM-1197826
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1197826