Bull. Korean Math. Soc. 2011; 48(4): 737-757
Printed July 1, 2011
https://doi.org/10.4134/BKMS.2011.48.4.737
Copyright © The Korean Mathematical Society.
Dong-Hoon Shin
Korea University
This work is concerned with an optimal selling rule for a large position of stock in a market. Selling a large block of stock in a short period typically depresses the market, which would result in a poor filling price. In addition, the large selling intensity makes the regime more likely to be poor state in the market. In this paper, regime switching and depressing terms associated with selling intensity are considered on a set of geometric Brownian models to capture movements of underlying asset. We also consider the liquidation strategy to sell much smaller number of shares in a long period. The goal is to maximize the overall return under state constraints. The corresponding value function with the selling strategy is shown to be a unique viscosity solution to the associated HJB equations. Optimal liquidation rules are characterized by a finite difference method. A numerical example is given to illustrate the result.
Keywords: regime switching, optimal selling rule, optimal control, HJB equation, viscosity solution
MSC numbers: 91G80
2020; 57(2): 311-330
2019; 56(5): 1355-1376
2015; 52(4): 1185-1199
2014; 51(3): 847-862
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd