Stochastic Control of Corporate Investment when Output Affects Future Prices
用随机控制理论求解企业在产出影响未来价格时的动态投资策略，提出一种计算高效的方法来同时解决投资与估值问题，适用于多企业博弈场景。
The advance of the theory of contingent claim pricing has made it possible to model and analyze very complex financial claims. When the value ofthe firm can be represented as a contingent then the firm's optimal financial policy can be determined with only a slight modification in standard solution techniques for contingent claims. In this paper, stochastic control theory is used to determine a dynamic investment policy for the valuemaximizing firm. The value of future, stochastic economic rents (i.e., the net present value ofthe firm), and the firm's optimal investment policy must reflect a rational reaction on behalf of its competitors. A computationally efficient methodology is presented for solving the simultaneous investment-valuation problem for an ?-firm game. The primary objectives of this paper are, first, to present a computationally efficient methodology for solving stochastic control problems that arise in the formulation of financial policy, and, second, to apply stochastic control to the firm's problem of finding a dynamic investment policy that maximizes firm value. The value of the firm is modeled as a continuous time contingent claim, which is traded in a financial market that is perfect, complete, and free of riskless arbitrage opportunities. In such a world, the financial policy of the firm should be designed to maximize firm value. The contingent claim pricing model provides sufficient versatility to incorporate diverse policy issues such as firm size, asset mix, capital structure, dividend policy, and basic existence issues such as reorganization and liquidation. This paper examines the optimal investment policy for a firm when the firm's output decision, via total industry output, affects the evolution of output prices. The investment problem considered here is similar to the optimal control problem of Pindyck [28]. Pindyck analyzes the optimal labor/capital mix in the presence of investment adjustment costs and a stochastic demand schedule in