英文标题：
《Turnpike Property and Convergence Rate for an Investment Model with
  General Utility Functions》
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作者：
Baojun Bian, Harry Zheng
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最新提交年份：
2014
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英文摘要：
  In this paper we aim to address two questions faced by a long-term investor with a power-type utility at high levels of wealth: one is whether the turnpike property still holds for a general utility that is not necessarily differentiable or strictly concave, the other is whether the error and the convergence rate of the turnpike property can be estimated. We give positive answers to both questions. To achieve these results, we first show that there is a classical solution to the HJB equation and give a representation of the solution in terms of the dual function of the solution to the dual HJB equation. We demonstrate the usefulness of that representation with some nontrivial examples that would be difficult to solve with the trial and error method. We then combine the dual method and the partial differential equation method to give a direct proof to the turnpike property and to estimate the error and the convergence rate of the optimal policy when the utility function is continuously differentiable and strictly concave. We finally relax the conditions of the utility function and provide some sufficient conditions that guarantee the turnpike property and the convergence rate in terms of both primal and dual utility functions.
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中文摘要：
在本文中，我们的目标是解决长期投资者在高财富水平下拥有幂型效用所面临的两个问题：一个是收费公路性质是否仍然适用于不一定可微或严格凹的一般效用，另一个是收费公路性质的误差和收敛速度是否可以估计。我们对这两个问题都给出了肯定的答案。为了得到这些结果，我们首先证明了HJB方程存在一个经典解，并给出了该解的对偶函数表示。我们用一些用试错法难以解决的非平凡例子来证明这种表示法的有用性。然后，我们结合对偶方法和偏微分方程方法，直接证明了收费公路的性质，并估计了当效用函数连续可微且严格凹时，最优策略的误差和收敛速度。最后，我们放松了效用函数的条件，并给出了一些充分条件，以保证收费公路性质以及原始和对偶效用函数的收敛速度。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Economics        经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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