A reinsurance game between two insurance companies with nonlinear risk processes

A non-zero-sum reinsurance-investment game with delay and asymmetric information

“…Under the objective of maximizing the utility of the relative performance, [6] studied a non-zero-sum stochastic differential investment and reinsurance game between two insurers whose surplus processes were modulated by continuous-time Markov chains; [37] considered a reinsurance and investment game between two insurers who have different opinions about some extra information. More studies on stochastic differential game problem may be found in [31], [33], [21], [14], [13], etc. In this paper, we consider a non-zero-sum stochastic differential reinsurance and investment game problem between two insurers.…”

Stochastic Differential Games Between Two Insurers With Generalized Mean-Variance Premium Principle

“…Inspired by Epsinosa and Touzi 2013, Bensoussan et al (2014), Meng et al (2015) and , we assume that both insurers' objectives are to maximize their expected utilities of relative performance at the terminal time T. That is, given the strategy π m of insurer m (m = 1 or 2), the other insurer k will choose an admissible investment-reinsurance strategy…”

“…Case (i) when α 1 = α 2 = 1, Problem 3 becomes a zero-sum game (see Browne (2000), Zeng (2010) and Zeng and Luo (2013)); Case (ii) when α 1 α 2 < 1 and α 1 + α 2 > 0, Problem 3 defines a non-zero sum game between the two insurers (see Bensoussan et al (2014), Meng et al (2015)); Case (iii) when α 1 = α 2 = 0, both insurers are indifferent about each other and Problem 3 retreats to two single-player problems (see Zhang et al (2016)).…”

“…They assume that each insurer has different utility function and that both insurers' surpluses are modulated by a continuous-time Markov chain and a marketindex. In this line, Meng et al (2015) consider an optimal reinsurance problem when the two insurers' surpluses are subject to quadratic risk controls. consider a reinsurance game problem for two ambiguity-averse insurers and obtain equilibrium under a worst-case scenario framework for the exponential utility functions.…”

Stackelberg Equilibrium Premium Strategies for Push-Pull Competition in a Non-Life Insurance Market with Product Differentiation

“…Zeng (2010), Taksar and Zeng (2011), and Jin et al (2013) consider Nash equilibria of stochastic differential games between insurance companies in reinsurance strategies. The analysis has been extended to non-zero sum games and additional investment controls by Bensoussan et al (2014), nonlinear risk processes by Meng et al (2015), ambiguity-aversion by Pun and Wong (2016), and insurance companies with different levels of trust in information by Yan et al (2017). Stackelberg-type equilibria of stochastic differential games have been studied in Lin et al (2012), where an insurance company selects an investment strategy while the market (or nature) selects a worst-case probability scenario, and in Chen and Shen (2018), where the game is between insurer and reinsurer, but not as here in a game between insurance companies.…”