状态依赖效用
State Dependent Utility
摘要：
我们提出了一种新的方法，是一致的状态依赖的公用事业。在我们的模型中，效用反映了未来现金流的消费满意度水平，因为它们是在经济主体做出消费和投资决策时被估值的。用于该模型的理论框架是作者在Dynamic State Tameness {arXiv：math.PR/0509139}中提出的理论框架。所提出的框架是布朗流理论的推广，并且可以应用于经典It^o随机微分方程解的过程，即使对于某些$δ>0$，波动和漂移只是局部$δ$ -Holder连续的.我们发展了鞅方法来解决最优消费和投资问题。完整的解决方案的最优消费和投资组合的问题得到了在一个非常一般的设置，其中包括几个功能形式的公用事业在目前的文献中，并考虑一般的限制最小的财富。作为第二个结果，我们得到了一个合适的表示直接数值计算的最优消费和投资策略。
英文摘要：
We propose a new approach to utilities that is consistent with state-dependent utilities. In our model utilities reflect the level of consumption satisfaction of flows of cash in future times as they are valued when the economic agents are making their consumption and investment decisions. The theoretical framework used for the model is one proposed by the author in Dynamic State Tameness {arXiv:math.PR/0509139}. The proposed framework is a generalization of the theory of Brownian flows and can be applied to those processes that are the solutions of classical It^o stochastic differential equations, even when the volatilities and drifts are just locally $δ$-Holder continuous for some $δ>0$. We develop the martingale methodology for the solution of the problem of optimal consumption and investment. Complete solutions of the optimal consumption and portfolio problem are obtained in a very general setting which includes several functional forms for utilities in the current literature, and consider general restrictions on minimal wealths. As a secondary result we obtain a suitable representation for straightforward numerical computations of the optimal consumption and investment strategies.
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