# A Parallel Monte Carlo Algorithm for the Life Cycle Asset Allocation Problem
## 1 Introduction  
In the expansive field of computational finance, the topic of life cycle asset allocation stands out as particularly significant. This is especially true given its alignment with the evolving third pillar of China's pension system--a current area of vulnerability. In the context of China's pension system, the application of life cycle asset allocation is particularly crucial. It not only represents an innovation in traditional pension management models but also serves as a vital approach to addressing current system challenges and enhancing the level of retirement security. The Chinese pension system is primarily composed of three pillars: the first pillar is the Basic Pension Insurance, which has broad coverage but limited benefit levels; the second pillar includes Enterprise Annuities and Occupational Annuities, which, despite achieving certain results, have relatively narrow coverage and face issues such as a limited fund scale and imbalanced development structure; the third pillar consists of supplementary pension insurance represented by personal pensions, which is still in its early stages with enormous potential. However, this system faces numerous challenges. Firstly, life insurance products are highly homogenized, failing to meet the diverse needs of retirement. Many products lack innovation in their design, with underlying assets heavily reliant on fixed-income products such as bonds and time deposits. In the current context of global economic slowdown and continuously declining interest rates, the sustainability of these products is under severe threat. Low yields are insufficient to effectively counteract inflation, which, over time, will erode the real purchasing power of pensions and affect the quality of life of the elderly. Therefore, to address this shortcoming and manage potential future marketrisks, the development of personalized pension products that balance returns and risks is urgently needed. Life cycle asset allocation is precisely such a strategy. Optimal asset allocation strategies involve the glide path concept [1], which refers to calculating the changing annual investment proportion in risky assets based on the specific life cycle and financial market of the investor throughout an investor's life cycle. The optimal problem is typically modeled as a stochastic process, examined through a set of inter-connected random variables, such as the Markov process. The development of algorithms calculating for glide path and efficient problem-solving for these models is increasingly emphasized due to the complex nature of life cycle asset allocation. Historically, the foundational work in classical life cycle fund models was initiated with [PERSON]'s mean-variance model [2], which pioneered the integration of mathematical statistics into effective asset allocation within modern investment theories. This was extended by [PERSON] [3], who proposed the life cycle hypothesis, suggesting that investors should strategically manage their consumption and investment throughout their lifespan with a view toward future earnings. Building on this, numerous academics have further developed life cycle investment mechanisms, providing effective investment guidance and ensuring retirement security. A significant advancement in life cycle fund development was achieved by [PERSON] [4], who advocated the use of utility functions to capture the investment and consumption preferences of individual investors. This was enhanced by [PERSON] et al. [5], who emphasized the critical relationship between an investor's income and their investment decisions by incorporating human capital considerations. This perspective suggests that younger investors, with greater career flexibility, are likely to have a higher tolerance for risk. Moreover, various models based on life cycle investment strategies, such as those by [PERSON] et al. [6] and [PERSON] et al. [7], have gained significant recognition. [PERSON], [PERSON] et al. [8; 9] introduced borrowing constraints and request motives.