# American Institute of Mathematical Sciences

October  2018, 14(4): 1323-1348. doi: 10.3934/jimo.2018009

## Optimal investment and dividend payment strategies with debt management and reinsurance

 1 School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China 2 Centre for Actuarial Studies, Department of Economics, The University of Melbourne, VIC 3010, Australia 3 School of Statistics, Faculty of Economics and Management, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China

* Corresponding author

Received  August 2016 Revised  October 2017 Published  January 2018

Fund Project: This work was supported by Program of Shanghai Subject Chief Scientist (14XD1401600), the 111 Project (B14019), National Natural Science Foundation of China (11601157,11601320,11571113,11231005,11501211), Research Grants Council of the Hong Kong Special Administrative Region (project No. HKU 17330816) and Faculty Research Grant by The University of Melbourne

This paper derives the optimal debt ratio, investment and dividend payment strategies for an insurance company. The surplus process is jointly determined by the reinsurance strategies, debt levels, investment portfolios and unanticipated shocks. The objective is to maximize the total expected discounted utility of dividend payments in finite-time period subject to three control variables. The utility functions are chosen as the logarithmic and power utility functions. Using dynamic programming principle, the value function is the solution of a second-order nonlinear Hamilton-Jacobi-Bellman equation. The explicit solution of the value function is derived and the corresponding optimal debt ratio, investment and dividend payment strategies are obtained. In addition, the investment borrowing constraint, dividend payment constraint and impacts of reinsurance policies are considered and their impacts on the optimal strategies are analyzed. Further, to incorporating the interest rate risk, the problem is studied under a stochastic interest rate model.

Citation: Qian Zhao, Zhuo Jin, Jiaqin Wei. Optimal investment and dividend payment strategies with debt management and reinsurance. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1323-1348. doi: 10.3934/jimo.2018009
##### References:

show all references