养老金储蓄管理中Hamilton-Jacobi-Bellman方程的弱非线性分析
Weakly nonlinear analysis of the Hamilton-Jacobi-Bellman equation arising from pension savings management
摘要：
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决方案。我们展示了如何在养老基金投资组合的管理中的最优股票债券比例的问题，可以制定的Hamilton-Jacobi-Bellman方程的解决方案。我们从定性和定量的角度分析解决方案。我们构造有用的边界的解决方案产生的最佳价值的股票债券比例的投资组合的估计。此外，我们构造了一个小的模型参数的解的渐近展开。最后，我们进行灵敏度分析的最优解相对于各种模型参数，并比较本文的分析结果与相应的已知结果所产生的时间离散动态随机优化模型。
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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