Abstract The optimal dividend payment problem in an insurance company whose surplus follows the classical Cram′er-Lundberg process with cluster claims is considered. A Hawkes process is
introduced so that the occurrence of a claim in the risky asset price triggers more sequent jumps.
Using dynamic programming principle and viscosity solution theory, it shows that the optimal value
function is a viscosity solution of the associated Hamilton-Jacobi-Bellman(HJB) equation. The optimal value function can be characterized as the smallest viscosity supersolution of the HJB equation.
Finally, some numerical results are exhibited and a barrier line strategy is introduced.
CHEN Yi-ling, BIAN Bao-jun. Optimal dividend payment in an insurance company with stationary Hawkes process. Applied Mathematics A Journal of Chinese Universities, 2020, 35(2): 158-168.
