A stochastic differential game for quadratic-linear diffusion processes. (11th January 2017)

• Record Type: Journal Article
• Authors: Luo, Shangzhen
• Is Part Of: Advances in applied probability. Volume 48:Number 4(2016)
• Page Start: 1161
• Page End: 1182
• Publication Date: 2017-01-11
• Subjects: Stochastic differential game, -- Nash equilibrium, -- Fleming–Bellman–Isaacs equations, -- quadratic-linear diffusion process; Primary 60G40, -- Secondary 93E20; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2016.69
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract: In this paper we study a stochastic differential game between two insurers whose surplus processes are modelled by quadratic-linear diffusion processes. We consider an exit probability game. One insurer controls its risk process to minimize the probability that the surplus difference reaches a low level (indicating a disadvantaged surplus position of the insurer) before reaching a high level, while the other insurer aims to maximize the probability. We solve the game by finding the value function and the Nash equilibrium strategy in explicit forms.