• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.737-757
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• 2011

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.

• The Pure and Applied Mathematics
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• v.18 no.2
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• pp.129-139
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• 2011

We consider an optimal trading rule in this paper. We assume that the underlying asset follows a mean-reverting process and the transaction consists of one buying and one selling. To maximize the profit, we find price levels to buy low and to sell high. Associated HJB equations are used to formulate the value function. A verification theorem is provided for sufficient conditions. We conclude the paper with a numerical example.

• Journal of Korean Institute of Industrial Engineers
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• v.41 no.5
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• pp.447-452
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• 2015

This paper considers a two-stage make-to-stock production system. The first stage produces a single-component and the second stage produces a make-to-stock product using components. In addition to internal demands, the first stage faces external demands with the option of accepting or rejecting. To ration component inventory, the manufacturer adopts a static rule. This paper analyzes the production controls at both facilities that maximizes the manufacturer's profit. Using the Markov decision process model, we characterize the optimal production policy by two monotonic switching curves.