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Searching for Answers to the Maintenance Problem of Insufficiently Financed, Financially Dependent Pension Funds through Stochastic Diffusion Processes

机译:通过随机扩散过程寻找资金不足,财务依赖的养老基金维持问题的答案

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摘要

The generic case of pensions fund that it is not sufficiently auto financed and it is thoroughly maintained with an external financing effort is considered in this chapter. To represent the unrestricted reserves value process of this kind of funds, a time homogeneous diffusion stochastic process with finite expected time to ruin is proposed. Then it is projected a financial tool that regenerates the diffusion at some level with positive value every time the diffusion hits a barrier placed at the origin. So, the financing effort can be modeled as a renewal-reward process if the regeneration level is preserved constant. The perpetual maintenance cost expected values and the finite time maintenance cost evaluations are studied. An application of this approach when the unrestricted reserves value process behaves as a generalized Brownian motion process is presented.
机译:本章考虑了一般情况下的养老金基金,它没有足够的自动融资,并且在外部融资的帮助下得到了充分维护。为了表示这类基金的无限制准备金过程,提出了具有预期破坏时间的有限时间均质扩散随机过程。然后,设计了一种金融工具,每次扩散到达原始位置的障碍时,该扩散工具都会在一定程度上以正值重新生成扩散。因此,如果再生水平保持不变,则可以将筹资工作建模为更新奖励过程。研究了永久性维护成本期望值和有限时间维护成本评估。提出了当无限制储备价值过程表现为广义布朗运动过程时该方法的应用。

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