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本文研究了随机最优控制下的投入决策问题,此问题的研究始于Merton的许多开创性的工作([1],[2],[3],[4])。Merton把投资决策问题变成一数学控制问题,从而利用随机控制理论和方法加以解决。在文献([5],[6],[7],[8],[9])中对最优投资决策问题中的效益期望做了一定的研究,在文献([10],[11],[12],[13])中讨论了Va-sicek模型下短期利率的期权定价问题,本文将几个好的结果加以组合,使随机最优控制下的投入决策问题的结论更加系统化。
This paper studies the input decision-making under stochastic optimal control. The research of this problem started with many pioneering work by Merton ([1], [2], [3], [4]). Merton turns the investment decision problem into a mathematical control problem, which is solved by stochastic control theory and method. In the literature ([5], [6], [7], [8], [9]), some research has been made on the expected benefits in the optimal investment decision-making. , [12], [13]), the short-term interest rate option pricing under the Va-sicek model is discussed. In this paper, several good results are combined to make the conclusion of the investment decision-making under the stochastic optimal control more systematic.