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摘要翻译：
本文的主要目的是分析一个完全非线性抛物型方程的最优投资组合构造问题的解。本文用Hamilton-Jacobi-Bellman方程的解来描述养老基金投资组合管理中的最优股票-债券比例问题。我们从定性和定量的角度分析了解决方案。我们构造了有用的解的界，得到了投资组合中股票与债券比例的最优值的估计。此外，我们用一个小的模型参数构造了解的渐近展开式。最后，对最优解对各种模型参数的敏感性进行了分析，并将本文的分析结果与已知的时间离散动态随机优化模型的结果进行了比较。
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英文标题：
《Weakly nonlinear analysis of the Hamilton-Jacobi-Bellman equation
arising from pension savings management》
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作者：
Zuzana Macova, Daniel Sevcovic
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最新提交年份：
2009
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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：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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英文摘要：
The main purpose of this paper is to analyze solutions to a fully nonlinear parabolic equation arising from the problem of optimal portfolio construction. We show how the problem of optimal stock to bond proportion in the management of pension fund portfolio can be formulated in terms of the solution to the Hamilton-Jacobi-Bellman equation. We analyze the solution from qualitative as well as quantitative point of view. We construct useful bounds of solution yielding estimates for the optimal value of the stock to bond proportion in the portfolio. Furthermore we construct asymptotic expansions of a solution in terms of a small model parameter. Finally, we perform sensitivity analysis of the optimal solution with respect to various model parameters and compare analytical results of this paper with the corresponding known results arising from time-discrete dynamic stochastic optimization model.
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PDF链接：
https://arxiv.org/pdf/0905.0155
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