Investment and consumption without commitment
Investment and consumption without commitment
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DOI：
10.1007/s11579-008-0014-6
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发表时间：
2007-08
影响因子：
1.6
通讯作者：
I. Ekeland;T. Pirvu
中科院分区：
文献类型：
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作者：
I. Ekeland;T. Pirvu
本文研究了非指数折现条件下的Merton投资组合管理问题。这就导致了决策者的时间不一致。如果时间= 0时的决策者可以委托她的继任者，她可以选择从她的角度来看最优的政策，并约束其他人遵守它，尽管他们并不认为这对他们来说是最优的。在不存在承诺机制的情况下，必须寻求连续决策者之间的子博弈完美均衡政策。在Ekeland和Lazrak （Preprint, 2006）的早期工作中，我们给出了有限视界下投资组合管理问题背景下均衡政策的精确定义。我们用一个偏微分方程组来描述它们，并在CRRA效用的情况下证明了它们的存在性。给出了对数效用情况下的显式解。我们还研究了无限视界情况，并为CRRA效用提供了两种不同的均衡策略（与指数贴现情况相比，其中只有一个最优策略）。我们的一些结果是在假设折扣函数(t)是两个指数的线性组合，或者是一个指数与一个线性函数的乘积的情况下证明的。
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 timet= 0 can commit her successors, she can choose the policy that is optimal from 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 policy between the successive decision-makers. In the line of the earlier work by Ekeland and Lazrak (Preprint, 2006) we give a precise definition of equilibrium policies in the context of the portfolio management problem, with finite horizon. We characterize them by a system of partial differential equations, and establish their existence in the case of CRRA utility. An explicit solution is provided for the case of logarithmic utility. We also investigate the infinite-horizon case and provide two different equilibrium policies for CRRA utility (in contrast with the case of exponential discounting, where there is only one optimal policy). Some of our results are proved under the assumption that the discount functionh(t) is a linear combination of two exponentials, or is the product of an exponential by a linear function.