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

Dingjun Yao; Rongming Wang; Lin Xu

doi:10.3934/jimo.2015.11.461

Article Contents

2015, Volume 11, Issue 2: 461-478. Doi: 10.3934/jimo.2015.11.461

This issue Previous Article Service investment and consumer returns policy in a vendor-managed inventory supply chain Next Article The EPQ model with deteriorating items under two levels of trade credit in a supply chain system

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: July 31, 2012

Revised: March 31, 2014

Published: March 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 93E20; Secondary: 62P05.

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