Robust Non-Zero-Sum Stochastic Differential Investment-Reinsurance Game

26 Pages Posted: 8 Mar 2016 Last revised: 8 May 2017

See all articles by Chi Seng Pun

Chi Seng Pun

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences

Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics

Date Written: March 8, 2016

Abstract

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 investment and reinsurance decision under relative performance concerns. Each AAI invests in a risky asset and a risk-free asset, and 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 and the Heston model, we solve the equilibrium strategies explicitly. Numerical studies are conducted to draw economic interpretations.

Keywords: Investment and Reinsurance, Non-Zero-Sum Stochastic Differential Game, Relative Performance Concerns, Model Uncertainty, Hamiltonian-Jacobi-Bellman-Isaacs Equation, Nash Equilibrium, Stochastic Factor

JEL Classification: C61, C62, C72, G22

Suggested Citation

Pun, Chi Seng and Wong, Hoi Ying, Robust Non-Zero-Sum Stochastic Differential Investment-Reinsurance Game (March 8, 2016). Insurance: Mathematics and Economics, Vol. 68, Pages 169-177, 2016, Available at SSRN: https://ssrn.com/abstract=2744495 or http://dx.doi.org/10.2139/ssrn.2744495

Chi Seng Pun (Contact Author)

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences ( email )

SPMS-MAS-05-22
21 Nanyang Link
Singapore, 637371
Singapore
(+65) 6513 7468 (Phone)

HOME PAGE: http://personal.ntu.edu.sg/cspun/

Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics ( email )

Shatin, N.T.
Hong Kong

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