Faculty Publications

Stochastic Differential Reinsurance Games In Diffusion Approximation Models

Document Type

Article

Keywords

Excess-of-loss reinsurance, Exit probability game, FBI equations, Nash equilibrium, Nonexistence of value, Proportional reinsurance

Journal/Book/Conference Title

Journal of Computational and Applied Mathematics

Volume

386

Abstract

In this paper, we study some noncooperative and cooperative stochastic differential games between two insurers with reinsurance controls. The surplus processes are modeled by diffusion approximation processes and the insurers can purchase reinsurance dynamically (i.e. control the drift and diffusion terms continuously over time). We consider two types of reinsurance: quota-share (QS) reinsurance and excess-of-loss (XL) reinsurance. In the noncooperative game, one insurer tries to minimize the probability that the surplus difference of the two insurers reaches a low target before it hits a high target, while the other aims to maximize the probability. We consider two cases of the game: in the first case, both insurers purchase XL reinsurance; and in the second case, one insurer purchases QS reinsurance while the other purchases XL reinsurance. In some parameter cases, we solve the game by finding the value function and Nash equilibrium strategy explicitly. In some parameter cases, the value function and Nash equilibrium strategy do not exist and we find the sup-value and sub-value functions of the game. We also establish and solve a cooperative game in which both insurers make joint efforts to minimize the probability that the sum of surplus processes reaches a low target before it hits a high target. Numerical examples and economic implications are given to illustrate the results.

Department

Department of Mathematics

Original Publication Date

4-1-2021

DOI of published version

10.1016/j.cam.2020.113252

Repository

UNI ScholarWorks, Rod Library, University of Northern Iowa

Language

en

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