摘要翻译：
本文研究了非指数贴现情形下的Merton投资组合管理问题。这就产生了决策者的时间不一致。如果决策者在时间t=0时可以承诺他/她的继任者，他/她可以选择从他/她的角度来看是最优的政策，并约束其他人遵守该政策，尽管他们并不认为该政策对他们来说是最优的。如果没有承诺机制，就必须在连续的决策者之间寻求一个子博弈--完美均衡策略。本文借鉴Ekeland和Lazrak的工作，在有限时域下给出了均衡策略的精确定义，并用偏微分方程组刻画了均衡策略，证明了在效用为CRRA且终端时间T较小时均衡策略的存在性。我们还研究了无限时域情形，在效用为CRRA的情形下给出了两种不同的显式解（与指数折扣的情形相比，指数折扣只有一个）。在假设折扣函数h(t)是两个指数的线性组合或指数与线性函数的乘积的情况下，证明了我们的一些结果。
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英文标题：
《Investment and Consumption without Commitment》
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作者：
Ivar Ekeland and Traian A. Pirvu
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最新提交年份：
2007
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
  In this paper, we investigate the Merton portfolio management problem in the context of non-exponential discounting. This gives rise to time-inconsistency of the decision-maker. If the decision-maker at time t=0 can commit his/her successors, he/she can choose the policy that is optimal from his/her point of view, and constrain the others to abide by it, although they do not see it as optimal for them. If there is no commitment mechanism, one must seek a subgame-perfect equilibrium strategy between the successive decision-makers. In the line of the earlier work by Ekeland and Lazrak we give a precise definition of equilibrium strategies in the context of the portfolio management problem, with finite horizon, we characterize it by a system of partial differential equations, and we show existence in the case when the utility is CRRA and the terminal time T is small. We also investigate the infinite-horizon case and we give two different explicit solutions in the case when the utility is CRRA (in contrast with the case of exponential discount, where there is only one). Some of our results are proved under the assumption that the discount function h(t) is a linear combination of two exponentials, or is the product of an exponential by a linear function.
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PDF链接：
https://arxiv.org/pdf/0708.0588