MAP20150023698Meng, HuiA Reinsurance game between two insurance companies with nonlinear risk processes / Hui Meng, Shuanming Li, Zhuo JinSumario: 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 HamiltonJacobiBellman 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 functionEn: Insurance : mathematics and economics. - Oxford : Elsevier, 1990- = ISSN 0167-6687. - 04/05/2015 Volumen 62 - mayo 2015 I. Título.
