Stochastic Stackelberg differential games between an insurer and a reinsurer
- Stochastic Stackelberg differential games between an insurer and a reinsurer
- 2017-12-29 11:00-12:00
沈洋博士现为加拿大约克大学数学与统计系助理教授。他于2014年在澳大利亚麦考瑞大学取得精算学博士学位，2011年在北京大学取得应用数学硕士学位，2009年于华东师范大学取得学士学位。主要研究方向为精算和金融数学，随机控制及其应用。已发表30余篇论文在Insurance: Mathematics and Economics, Scandinavian Actuarial Journal, Automatica, Quantitative Finance, European Journal of Operational Research, Annals of Operations Research等杂志。
This paper proposes a new continuous-time framework to analyze optimal reinsurance, in which an insurer and a reinsurer are two players of a stochastic Stackelberg differential game, i.e., a stochastic leader-follower differential game. This allows us to determine optimal reinsurance from joint interests of the insurer and the reinsurer, which is rarely considered in a continuous-time setting. In the Stackelberg game, the reinsurer moves first and the insurer moves subsequently to achieve a Stackelberg equilibrium towards optimal reinsurance arrangement. Speaking more precisely, the reinsurer is the leader of the game and decides on optimal reinsurance premium to charge, while the insurer is the follower of the game and chooses optimal proportional reinsurance to purchase. We solve the game problem in two cases: exponential utility maximization and mean-variance optimization. We find that the reinsurer always applies the variance premium principle to calculate the optimal reinsurance premium and the insurer's optimal ceding/retained proportion of insurance risk depends not only on the risk aversion of itself but also on that of the reinsurer.