The estimated localities of these regions are also provided.įunding: This work was supported by the Hong Kong Research Grants Council, the Guangdong Basic and Applied Basic Research Foundation, the National Natural Science Foundation of China, the PolyU-SDU Joint Research Center on Financial Mathematics, the CAS AMSS-PolyU Joint Laboratory of Applied Mathematics, and Hong Kong Polytechnic University. The insurance company should be exposed to a higher risk as its surplus increases, be exposed to the entire risk once its surplus upward crosses the reinsurance barrier, and pay out all its reserves exceeding the dividend-payout barrier. We find that the surplus-time space can be divided into three nonoverlapping regions by a risk-magnitude and time-dependent reinsurance barrier and a time-dependent dividend-payout barrier. We obtain the C2,1 smoothness of the value function and a comparison principle for its gradient function by the penalty approximation method so that one can establish an efficient numerical scheme to compute the value function. This is a mixed singular–classical stochastic control problem, and the corresponding Hamilton–Jacobi–Bellman equation is a variational inequality with a fully nonlinear operator and subject to a gradient constraint. The company is allowed to buy reinsurance contracts dynamically over the whole time horizon to cede its risk exposure with other reinsurance companies. The goal of the company is to maximize the expected cumulative discounted dividend payouts until bankruptcy or maturity, whichever comes earlier. Full coverage of continuous and discrete systems (including cellular automata, etc.This paper studies a dynamic optimal reinsurance and dividend-payout problem for an insurance company in a finite time horizon.
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