# A Parallel Monte Carlo Algorithm for the Life Cycle Asset Allocation Problem
## 2 Materials and Methods
### Life Cycle Asset Allocation Model
#### 2.1.3 Labor Income Patterns in China: Insights from the China General Social Survey (CGSS)  
Labor income is usually an important component of total assets. The growth rate of labor income from age \(t\) to \(t+1\) is given by \(g_{t}\). Two aspects of labor income present risk--the systematic volatility of labor income and the correlation between labor income growth and stock returns. Labor income \(Y_{t+1}\) earned at age \(t+1\) is shown below [31]:  
\[Y_{t+1}=Y_{t}\times\exp((S_{t+1}-S_{t})/S_{t}) \tag{6}\]  
where \(Y_{start}=1\); \(S_{t}\) is the labor income.  
To analyze current trends and patterns within the context of labor income dynamics, we use robust statistical methods to ensure accurate and insightful results. The China General Social Survey (CGSS) is one of the most comprehensive, continuous national social surveys conducted in China. In our study, we utilize the most recent dataset, specifically the 2021 data, to model labor income. The 2021 dataset provides a contemporary snapshot of the economic conditions influencing labor income, making it a vital resource for understanding the factors that impact earnings across different demographics and regions. We process the data by the age and the income columns, dropping the unavailable and the extreme sample points and computing the average labor income per year for investors in China. We use a degree 3 polynomial function to estimate labor income, \(S_{t}=-1745.40+141.43\times t-3.13\times t^{2}+0.021\times t^{3}\), shown in Figure 1.  
Many studies have hypothesized that real income follows a hump-like pattern, characterized by rapid growth until around age 35, a slower rise between ages 45 and 50, and a gradual decline thereafter. This pattern is widely accepted as a general model of income dynamics over the life cycle. However, through our detailed data cleaning and modeling of the China General Social Survey (CGSS), we have uncovered unique characteristics in the labor income trajectory of Chinese consumers, as depicted in the figure. The graph illustrates labor income against age, highlighting several key deviations from the expected pattern. Initially, labor income increases rapidly, reaching its peak earlier than the global average, around age 30-35. This peak is followed by a relatively sharp decline, contradicting the hypothesis of a slower rise until the age of 50. Instead, the data show a continuous decrease in labor income after the early thirties, which becomes more pronounced beyond the age of 40. By age 60, labor income levels are significantly lower, indicating a steep downward trend.  
This distinctive pattern can be attributed to several socio-economic factors unique to China, including retirement policies, the structure of the labor market, and cultural attitudes toward work and retirement. The earlier peak and subsequent decline suggest that Chinese workers may experience a more pronounced reduction in income as they age compared to their counterparts in other countries. Figure 1 visually presents these findings, emphasizing the rapid increase in labor income up to the early thirties, the peak around age 30-35, and the subsequent decline, highlighting the unique labor income trajectory of Chinese consumers. By examining these data, we can gain a deeper understanding of the economic behavior and challenges faced by Chinese workers throughout their careers.