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October  2018, 14(4): 1443-1461. doi: 10.3934/jimo.2018015

## Optimal liability ratio and dividend payment strategies under catastrophic risk

 1 School of Statistics, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China 2 Centre for Actuarial Studies, Department of Economics, The University of Melbourne, VIC 3010, Australia

* Corresponding author: Lyu Chen

Received  December 2016 Revised  August 2017 Published  January 2018

Fund Project: This work was supported by National Natural Science Foundation of China (11571113,11771147), the 111 Project(B14019) and Faculty Research Grant of University of Melbourne.

This paper investigates the optimal strategies for liability management and dividend payment in an insurance company. The surplus process is jointly determined by the reinsurance policies, liability levels, future claims and unanticipated shocks. The decision maker aims to maximize the total expected discounted utility of dividend payment in infinite time horizon. To describe the extreme scenarios when catastrophic events occur, a jump-diffusion Cox-Ingersoll-Ross process is adopted to capture the substantial claim rate hikes. Using dynamic programming principle, the value function is the solution of a second-order integro-differential Hamilton-Jacobi-Bellman equation. The subsolution--supersolution method is used to verify the existence of classical solutions of the Hamilton-Jacobi-Bellman equation. The optimal liability ratio and dividend payment strategies are obtained explicitly in the cases where the utility functions are logarithm and power functions. A numerical example is provided to illustrate the methodologies and some interesting economic insights.

Citation: Linyi Qian, Lyu Chen, Zhuo Jin, Rongming Wang. Optimal liability ratio and dividend payment strategies under catastrophic risk. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1443-1461. doi: 10.3934/jimo.2018015
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##### References:
Optimal liability ratio values versus $c$
Optimal liability ratio values versus $\mu$
Optimal liability ratio values versus $\sigma$
Optimal liability ratio values versus $\gamma$
Optimal liability ratio values versus $\theta$ for logarithmic utility function
Optimal liability ratio values versus $\theta$ for power utility function
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