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This article is concerned with a class of control systems with Markovian switching,in which an ltd formula for Markov-modulated processes is derived.Moreover,an optimal control law satisfying the generalized Hamilton-Jacobi-Bellman(HJB) equation with Markovian switching is characterized.Then,through the generalized HJB equation,we study an optimal consumption and portfolio problem with the financial markets of Markovian switching and inflation.Thus,we deduce the optimal policies and show that a modified Mutual Fund Theorem consisting of three funds holds.Finally,for the CRRA utility function,we explicitly give the optimal consumption and portfolio policies.Numerical examples are included to illustrate the obtained results. 相似文献
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随机微分方程理论在经济建模中的应用研究 总被引:3,自引:0,他引:3
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. 相似文献
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