随机微分方程理论在经济建模中的应用研究

A STUDY ON THE THEORY OF S. D. E. AND ITS APPLICATION IN ECONOMIC MODELLING

考虑投资者参与证券投资及消费．由于证券、价格的变动趋势受诸多因素的影响，显示出价格很不稳定．用随机微分方程来刻划证券价格的变动趋势是合理的．Ｋａｒａｔｚａｓ等人在［１］中研究了最优消费与投资的一般特性，而且在模型参数为常系数假设下给出了反馈形式的最优消费与投资公式．但模型系数都为常值的假设在实际应用中显然有很大的局限性．为此，本文就β（ｔ）为有限分段函数情形推广了Ｋａｒａｔｚａｓ等人的结果．所得结论比Ｋａｒａｔｚａｓ［１］所得结论更具有应用价值．

A general consumption/investment problem have been considered for an agent whose actions connot affact the market prices,and strives to maximize total expected discounted utility of both consumption and terminal wealth in [1]. Furthermore,Karatzas et al. in [1] have approached the case of market model with constant coefficients. We generalized the case with constant coefficients to general situation, where we suppose discount process β(t) to be finite piecewise function,and obtain the optimal portfolio and consumption rules which are derived very explicity in feedback form.