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An Optimal Portfolio Problem of DC Pension with Input-Delay and Jump-Diffusion Process
Mathematical Problems in Engineering ( IF 1.430 ) Pub Date : 2020-07-31 , DOI: 10.1155/2020/4343629
Weixiang Xu 1 , Jinggui Gao 1
Affiliation  

In this paper, an optimal portfolio control problem of DC pension is studied where the time interval between the implementation of investment behavior and its effectiveness (hereafter input-delay) is particularly focused. There are two assets available for investment: a risk-free cash bond and a risky stock with a jump-diffusion process. And the wealth process of the pension fund is modeled as a stochastic delay differential equation. To secure a comfortable retirement life for pension members and also avoid excessive risk, the fund managers in this paper aim to minimize the expected value of quadratic deviations between the actual terminal fund scale and a preset terminal target. By applying the stochastic dynamic programming approach and the match method, the optimal portfolio control problem is solved and the closed-form solution is obtained. In addition, an algorithm is developed to calculate the numerical solution of the optimal strategy. Finally, we have performed a sensitivity analysis to explore how the managers’ preset terminal target, the length of input-delay, and the jump intensity of risky assets affect the optimal investment strategy.

中文翻译:

具有输入时滞和跳-扩散过程的DC养老金最优投资组合问题

本文研究了DC养老金的最优投资组合控制问题,其中特别关注投资行为的实施与其有效性之间的时间间隔(以下称投入延迟)。有两种可用于投资的资产:无风险现金债券和具有跳跃扩散过程的有风险股票。养老基金的财富过程被建模为随机时滞微分方程。为了确保退休人员享有舒适的退休生活并避免过多的风险,本文中的基金经理旨在将实际最终基金规模与预设最终目标之间的二次方偏差的期望值最小化。通过应用随机动态规划方法和匹配方法,解决了最优投资组合控制问题,得到了闭式解。另外,开发了一种算法来计算最优策略的数值解。最后,我们进行了敏感性分析,以探讨管理者预设的最终目标,输入延迟的长度以及风险资产的跳跃强度如何影响最优投资策略。
更新日期:2020-07-31
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