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April  2015, 11(2): 461-478. doi: 10.3934/jimo.2015.11.461

## Optimal asset control of a geometric Brownian motion with the transaction costs and bankruptcy permission

 1 School of Finance, The Center of Cooperative Innovation for Modern Service Industry, Nanjing University of Finance and Economics, Nanjing 210023 2 School of Finance and Statistics, Research Center of International Finance and Risk Management, East China Normal University, Shanghai 200241 3 School of Mathematics and Computer Science, Anhui Normal University, Wuhu, Anhui, 241003

Received  August 2012 Revised  April 2014 Published  September 2014

We assume that the asset value process of some company is directly related to its stock price dynamics, which can be modeled by geometric Brownian motion. The company can control its asset by paying dividends and injecting capitals, of course both procedures imply proportional and fixed costs for the company. To maximize the expected present value of the dividend payments minus the capital injections until the time of bankruptcy, which is defined as the first time when the asset value falls below the regulation requirement $m$, we seek to find the joint optimal dividend payment and capital injection strategy. By solving the Quasi-variational inequalities, the optimal control problem is addressed, which depends on the parameters of the model and the costs. The sensitivities of transaction costs (such as tax, consulting fees) to the optimal strategy, the expected growth rate and volatility of the firm asset value are also examined, some interesting economic insights are included.
Citation: Dingjun Yao, Rongming Wang, Lin Xu. Optimal asset control of a geometric Brownian motion with the transaction costs and bankruptcy permission. Journal of Industrial & Management Optimization, 2015, 11 (2) : 461-478. doi: 10.3934/jimo.2015.11.461
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