英文标题：
《Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling》
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作者：
Nicole El Karoui (LPMA), Caroline Hillairet (CMAP), Mohamed Mrad
  (LAGA)
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最新提交年份：
2014
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英文摘要：
  The purpose of this paper relies on the study of long term yield curves modeling. Inspired by the economic litterature, it provides a financial interpretation of the Ramsey rule that links discount rate and marginal utility of aggregate optimal consumption. For such a long maturity modelization, the possibility of adjusting preferences to new economic information is crucial. Thus, after recalling some important properties on progressive utility, this paper first provides an extension of the notion of a consistent progressive utility to a consistent pair of progressive utilities of investment and consumption. An optimality condition is that the utility from the wealth satisfies a second order SPDE of HJB type involving the Fenchel-Legendre transform of the utility from consumption. This SPDE is solved in order to give a full characterization of this class of consistent progressive pair of utilities. An application of this results is to revisit the classical backward optimization problem in the light of progressive utility theory, emphasizing intertemporal-consistency issue. Then we study the dynamics of the marginal utility yield curve, and give example with backward and progressive power utilities.
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中文摘要：
本文的目的在于对长期收益率曲线建模的研究。受经济学理论的启发，它对拉姆齐法则进行了金融解释，拉姆齐法则将贴现率和总最优消费的边际效用联系起来。对于这种长期模型化，根据新的经济信息调整偏好的可能性至关重要。因此，在回顾了累进效用的一些重要性质之后，本文首先将一致累进效用的概念推广到投资和消费的一对一致累进效用。最优性条件是，来自财富的效用满足HJB型二阶SPDE，涉及消费效用的芬切尔-勒让德变换。求解该SPDE是为了给出这类一致渐进效用对的完整特征。这个结果的一个应用是根据渐进效用理论重新审视经典的反向优化问题，强调跨期一致性问题。然后，我们研究了边际效用-收益率曲线的动力学，并以落后和进步的电力公司为例。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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