Robust non-zero-sum stochastic differential reinsurance game

• Main Authors: Pun, Chi Seng, Wong, Hoi Ying
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2016
• Subjects: Non-zero-sum stochastic differential game; Relative performance concerns; Reinsurance; Model uncertainty; Hamiltonian–Jacobi–Bellman–Isaacs equation; Nash equilibrium
• Online Access: https://hdl.handle.net/10356/81378; http://hdl.handle.net/10220/40727
• Institution: Nanyang Technological University

This paper considers the non-zero-sum stochastic differential game problem between two ambiguity-averse insurers (AAIs) who encounter model uncertainty and seek the optimal reinsurance decision under relative performance concerns. Each AAI manages her own risks by purchasing reinsurance with the objective of maximizing the expected utility of her relative terminal surplus with respect to that of her counterparty. The two AAIs’ decisions influence each other through the insurers’ relative performance concerns and the correlation between their surplus processes. We establish a general framework of Nash equilibrium for the associated non-zero-sum game with model uncertainty. For the representative case of exponential utilities, we solve the equilibrium strategies explicitly. Numerical studies are conducted to draw economic interpretations.