资本配置与积累的统计场视角：个体动力学
A Statistical Field Perspective on Capital Allocation and Accumulation: Individual dynamics
AI总结：
本文用统计场方法研究异质性企业和投资者在背景场中的个体资本配置与积累动力学，揭示资本水平、部门竞争、股息与股价波动如何共同决定企业迁移和投资者再配置行为。
摘要：
我们在系列文章中已经表明，对大量经济主体的经典描述可以被统计场形式化方法所取代。为了更好地理解资本在不同部门之间的积累与配置，本文将这种统计场描述应用于大量被分为两组的异质性主体。第一组由不同部门中的大量企业组成，它们共同拥有全部实物资本。第二组是投资者，他们持有全部金融资本，并根据投资偏好、预期收益以及金融市场上股票价格的变化，将资本配置到各部门的企业之间。作为回报，企业向投资者支付股息。因此，金融资本是股息和股票估值的函数，而实物资本则是金融部门所配置总资本的函数。我们之前的工作侧重于描述潜在长期均衡的背景场，而本文则计算个体主体的转移函数，并研究他们在背景场中作为其初始状态函数的概率动力学。我们表明，资本积累取决于多种因素。与每家企业轨迹相关的概率是若干相互矛盾效应的结果：企业倾向于转向长期收益最大的部门，但必须考虑其转向在整个轨迹过程中对其对投资者吸引力的影响。由于该轨迹在很大程度上取决于转移部门的平均资本，企业在迁移过程中的吸引力取决于这些部门的资本相对水平。因此，一家资本不足的企业进入高资本部门将会经历吸引力的损失，并随后失去投资者。此外，企业还必须考虑中间部门竞争的影响。资本不足的企业往往会被排挤到平均资本较低的部门，而资本过剩的企业则倾向于转向平均资本较高的部门。对投资者而言，资本配置取决于他们的短期和长期收益。这些收益并非相互独立：在短期内，收益由企业股息和股票价格上涨共同构成；在长期内，收益基于企业的增长预期，同时也间接基于对更高股票价格的预期。投资者的资本配置直接取决于股票价格的波动性和企业的股息。投资者将倾向于重新配置资本，以最大化其短期和长期收益。他们的资本水平越高，重新配置的力度就越强。
英文摘要：
We have shown, in a series of articles, that a classical description of a large number of economic agents can be replaced by a statistical fields formalism. To better understand the accumulation and allocation of capital among different sectors, the present paper applies this statistical fields description to a large number of heterogeneous agents divided into two groups. The first group is composed of a large number of firms in different sectors that collectively own the entire physical capital. The second group, investors, holds the entire financial capital and allocates it between firms across sectors according to investment preferences, expected returns, and stock prices variations on financial markets. In return, firms pay dividends to their investors. Financial capital is thus a function of dividends and stock valuations, whereas physical capital is a function of the total capital allocated by the financial sector. Whereas our previous work focused on the background fields that describe potential long-term equilibria, here we compute the transition functions of individual agents and study their probabilistic dynamics in the background field, as a function of their initial state. We show that capital accumulation depends on various factors. The probability associated with each firm's trajectories is the result of several contradictory effects: the firm tends to shift towards sectors with the greatest long-term return, but must take into account the impact of its shift on its attractiveness for investors throughout its trajectory. Since this trajectory depends largely on the average capital of transition sectors, a firm's attractiveness during its relocation depends on the relative level of capital in those sectors. Thus, an under-capitalized firm reaching a high-capital sector will experience a loss of attractiveness, and subsequently, in investors. Moreover, the firm must also consider the effects of competition in the intermediate sectors. An under-capitalized firm will tend to be ousted out towards sectors with lower average capital, while an over-capitalized firm will tend to shift towards higher averagecapital sectors. For investors, capital allocation depends on their short and long-term returns. These returns are not independent: in the short-term, returns are composed of both the firm's dividends and the increase in its stock prices. In the long-term, returns are based on the firm's growth expectations, but also, indirectly, on expectations of higher stock prices. Investors' capital allocation directly depends on the volatility of stock prices and {\ldots}rms'dividends. Investors will tend to reallocate their capital to maximize their short and long-term returns. The higher their level of capital, the stronger the reallocation will be.
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