This paper investigates a collective defined contribution (CDC) pension fund scheme in continuous time, where members' contributions are fixed in advance, and benefit payments depend on the final salary rate. We take account of the co-integration between labor income and the stock market by letting the difference between logs of labor and dividends follow a mean-reverting process. Further, labor income is also a product of aggregate labor income and member's idiosyncratic shocks whose constant growth rate is unknown. It can be modeled by a continuous-time two-state hidden Markov chain. Further, the pension fund can be invested in the financial market consisting of one risky asset and one risk-free asset to enhance profits. After using Hamilton-Jacobi-Bellman (HJB) equations, the closed-form solutions for the optimal asset allocation and the benefit payment policies are obtained to maximize the social welfare and the terminal surplus wealth. Numerical examples are also conducted to illustrate the sensitivity of parameters on the optimal strategies.

中文翻译：

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股票市场和劳动力市场共同整合时的集体固定缴款计划的最佳策略


本文连续调查了集体固定缴款 （CDC） 养老基金计划，其中成员的缴款是预先固定的，福利支付取决于最终工资率。我们考虑了劳动收入和股票市场之间的协整，让劳动对数和股息对数之间的差异遵循均值回归过程。此外，劳动收入也是总劳动收入和成员特质冲击的乘积，其恒定增长率是未知的。它可以通过连续时间的二态隐马尔可夫链建模。此外，养老基金可以投资于由一种风险资产和一种无风险资产组成的金融市场，以提高利润。使用 Hamilton-Jacobi-Bellman （HJB） 方程后，得到最优资产配置的闭式解和福利支付政策，以实现社会福利和终端剩余财富的最大化。还进行了数值示例来说明参数对最佳策略的敏感性。