A Reinsurance and Investment Game between Two Insurers under the CEV Model. (21st August 2020)

• Record Type: Journal Article
• Authors: Zhang, Gongliang; Cheng, Shuo; Li, Ziye; Cao, Ming
• Other Names: Yu Wenguang Guest Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2020(2020)
• Publication Date: 2020-08-21
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2020/4696941
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : In this paper, the problem of nonzero-sum stochastic differential game between two competing insurance companies is considered, i.e., the relative performance concerns. A certain proportion of reinsurance can be taken out by each insurer to control his own risk. Moreover, each insurer can invest in a risk-free asset and risk asset with the price dramatically following the constant elasticity of variance (CEV) model. Based on the principle of dynamic programming, a general framework regarding Nash equilibrium for nonzero-sum games is established. For the typical case of exponential utilization, we, respectively, give the explicit solutions of the equilibrium strategy as well as the equilibrium function. Some numerical studies are provided at last which assist in obtaining some economic explanations.