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中文摘要：
衍生证券在实际交易中的买卖价格一般是不一样的。本文讨论了衍生证券买卖价格不同时的投资消费决策问题。以最大化投资者消费效用和终值效用为目标，建立模型。应用随机最优控制方法，分三种情形进行讨论，得到不同情形下一般效用函数的最优投资消费策略，还给出了幂效用函数情形的策略解析形式。最后，用数值例子说明了投资消费策略随着不同市场情形的变化情况。
英文摘要：
Derivatives are sold or bought at different prices in practice. Studied in this paper is an investment and consumption decision problem about derivatives with different sale price and purchase price. With maximizing the consumption utility and terminal wealth utility as goal, we establish the model. With stochastic optimization control theory, the problem is divided into three cases and the optimal investment and consumption strategies of three cases are presented, respectively. The explicit strategies are given for the power utility function. Finally a numerical example is given to illustrate the variation of strategies with the change of market.
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Multifractal analysis on international crude oil markets based on the multifractal detrended fluctua
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