# American Institute of Mathematical Sciences

March  2017, 7(1): 1-19. doi: 10.3934/mcrf.2017001

## Optimal size of business and dividend strategy in a nonlinear model with refinancing and liquidation value

 1 School of Statistics, Faculty of Economics and Management, East China Normal University, Shanghai 200241, China 2 School of Mathematics and Computer Sciences, Anhui Normal University, Wuhu 241000, China

* Corresponding author

Received  July 2015 Revised  February 2016 Published  December 2016

Fund Project: This work was supported by National Natural Science Foundation of China (11571113,11231005,11201006), Program of Shanghai Subject Chief Scientist(14XD1401600), the 111 Project (B14019), Education of Humanities and Social Science Fund Project (12YJC910012).

This paper investigates the optimal control problem with a nonlinear capital process attributed to internal competition factors. Suppose that the company can control its capital process by paying dividend, refinancing and changing the size of business. The transaction costs generated by the control processes as well as the liquidation value at ruin are considered. We aim at seeking the optimal control strategies for maximizing the company's value. The results show that the company should expand the business scale when the current capital increases. The refinancing may only happen at the moments when, and only when, the capital is null. The dividends should be paid out according to barrier strategy if the dividend rate is unconstrained or threshold strategy if the dividend rate is bounded, respectively.

Citation: Gongpin Cheng, Lin Xu. Optimal size of business and dividend strategy in a nonlinear model with refinancing and liquidation value. Mathematical Control & Related Fields, 2017, 7 (1) : 1-19. doi: 10.3934/mcrf.2017001
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