A reinsurance game between two insurance companies with nonlinear risk processes

Hui Meng, Shuanming Li*, Zhuo Jin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

37 Citations (Scopus)

Abstract

In this paper, we consider a stochastic differential reinsurance game between two insurance companies with nonlinear (quadratic) risk control processes. We assume that the goal of each insurance company is to maximize the exponential utility of the difference between its terminal surplus and that of its competitor at a fixed terminal time T. First, we give an explicit partition (including nine subsets) of time interval [0, T]. Further, on every subset, an explicit Nash equilibrium strategy is derived by solving a pair of Hamilton-Jacobi-Bellman equations. Finally, for some special cases, we analyze the impact of time t and quadratic control parameter on the Nash equilibrium strategy and obtain some simple partition of [0, T]. Based on these results, we apply some numerical analysis of the time t, quadratic control parameter and competition sensitivity parameter on the Nash equilibrium strategy and the value function.

Original languageEnglish
Pages (from-to)91-97
Number of pages7
JournalInsurance: Mathematics and Economics
Volume62
DOIs
Publication statusPublished - 1 May 2015
Externally publishedYes

Keywords

  • Exponential utility
  • Nash equilibrium
  • Nonlinear risk process
  • Relative performance
  • Stochastic differential game

Fingerprint

Dive into the research topics of 'A reinsurance game between two insurance companies with nonlinear risk processes'. Together they form a unique fingerprint.

Cite this