养老金计划的随机模型

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英文标题：
《Stochastic model of a pension plan》
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作者：
Paz Grimberg and Zeev Schuss
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最新提交年份：
2014
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英文摘要：
  Structuring a viable pension plan is a problem that arises in the study of financial contracts pricing and bears special importance these days. Deterministic pension models often rely on projections that are based on several assumptions concerning the \"average\" long-time behavior of the stock market. Our aim here is to examine some of the popular \"average\" assumptions in a more realistic setting of a stochastic model. Thus, we examine the contention that investment in the stock market is similar to gambling in a casino, while purchasing companies, after due diligence, is safer under the premise that acting as a holding company that wholly owns other companies avoids some of the stock market risks. We show that the stock market index faithfully reflects its companies\' profits at the time of their publication. We compare the shifted historical dynamics of the S\\&P500\'s aggregated financial earnings to its value, and find a high degree of correlation. We conclude that there is no benefit to a pension fund in wholly owning a super trust. We verify, by examining historical data, that stock earnings follow an exponential (geometric) Brownian motion and estimate its parameters. The robustness of this model is examined by an estimate of a pensioner\'s accumulated assets over a saving period. We also estimate the survival probability and mean survival time of the accumulated individual fund with pension consumption over the residual life of the pensioner.
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中文摘要：
构建一个可行的养老金计划是金融合同定价研究中出现的一个问题，目前具有特殊重要性。确定性养老金模型通常依赖于基于股票市场“平均”长期行为的若干假设的预测。我们的目标是在更现实的随机模型中检验一些流行的“平均”假设。因此，我们研究了一个论点，即股票市场投资类似于赌场赌博，而在尽职调查后，收购公司更安全，前提是作为全资拥有其他公司的控股公司，可以避免一些股票市场风险。我们表明，股票市场指数真实地反映了其公司在发布时的利润。我们比较了标普500指数累计财务收益的历史动态变化与其价值，并发现了高度的相关性。我们的结论是，完全拥有超级信托对养老基金没有好处。通过检验历史数据，我们验证了股票收益遵循指数（几何）布朗运动，并估计了其参数。该模型的稳健性通过估计养老金领取者在一个储蓄期内的累积资产来检验。我们还估计了在养老金领取者剩余寿命内，有养老金消费的累积个人基金的生存概率和平均生存时间。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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关键词：随机模型 养老金 Applications Differential Quantitative