The capital markets of emerging market economies are constantly improving. There have been many “financial anomalies” in the financial market that classical financial theories cannot explain, such as the economic Sunday effect, capital market price surge and sell-off, contrarian investment strategy, seasonal effect, etc. The “financial anomaly” results from the joint efforts of the majority of social investors’ trading behavior. This synergy is again a function of investors’ heterogeneous beliefs [1]. Therefore, studying investors’ heterogeneous views can create a new explanatory path for uncovering “financial anomalies” in capital markets. Since the traditional financial theory is based on rational expectations, financial anomalies cannot be solved by mathematical models. The theoretical framework of rational expectations is even more unable to form a reasonable explanation for the price fluctuations of funds, futures, bonds, and other financial markets other than the stock market [2]. Thus, behavioral finance was born in the 1980s. It draws on psychological concepts such as “overconfidence” and “heterogeneous belief” in psychology. It tries to analyze the phenomenon of finance and finance with behavioral psychology theory. This article will explore the volatility of securities prices in the asset market. The research results of this paper inject new theoretical resources into the capital pricing theory.

There are many types of financial capital and its derivative products available to investors in the natural capital market. Chinese capital market started late and is immature. Financial investors have different preferences and beliefs [3]. These factors will make the solid and efficient capital market theory unable to explain phenomenal financial problems. It cannot effectively solve the pricing problem of financial products. Therefore, we need to adjust the research premise of traditional economic theory. We make the following assumptions: (1) The capital market consists of assets such as risk-free assets (such as treasury bills) and risky assets (such as stocks). (2) The number of investors with overconfidence beliefs is N. They are less likely to invest in risky assets. Its behavior has a particular impact on capital pricing. (3) Investors complete the investment transaction in three stages: t=1, 2, and 3 when the market transaction cost is 0. The cash flow produced is equal to
_{n}^{−aWn}. Here a is the absolute risk aversion coefficient, and W is the wealth level. Our investor decision problem at time

Where _{t}_{−1} is the number of investors’ risky assets. The investor's amount of risk-free assets is given by _{ti}_{t}

Scenario 1: The investor decision at time t=3 can be transformed into:

We are based on the standard normal distribution principle and obtained from the above formula:

Optimizing the above equation shows that

The above _{0}[ ] and _{0} [ ] respectively represent the investor's investment expectation and its variance value under the belief of overconfidence [5]. According to the projection theorem, the expected value and its variance can be obtained as:

Therefore, the expected function value and covariance value of investor investment are expressed as follows:

Further results:

From the above function values of _{0}[ ] and _{0}[ ], the first-order optimal condition can be obtained as:

According to the principle of equilibrium of supply and demand in the capital market:

Scenario 2: The investor's decision at time t=2 can be transformed into:

We set the expected value of the investor's investment at this time to be _{3}. So the investor's optimal investment decision function at time t=2 is as follows:

According to the principle of investment equilibrium, the following functions can be obtained:

Combined with the projection theorem, we get:

The investment expectations of an investor with overconfidence heterogeneous beliefs at a price _{3} are as follows:

The above formula can be converted to:

According to formula (10) and the functional equations (6)~(9), the asset pricing model at time t=2 is:

According to the second part of the investor's investment decision and its equilibrium price model, it can be known that the investor's decision at time t=3 can be converted into formula (2). The asset pricing model is formula (6). And the investor's decision at time t=2 can be reversed into formula (7). The asset pricing model is formula (11). This article aims to obtain the investment characteristics of investors with different beliefs about the equilibrium price of assets. We consider the following differential equation:

Since this differential equation under

Suppose

Let
^{w24ψ(ω)},
_{1} = _{1} again. The above function can then be converted into a Weber differential equation:

According to the formal definition of the general solution of Weber's differential equation, we can get:

Here,

The positive solution of the function of formula (7) in this case

Correspondingly, the positive solution of the function of formula (7) in the case of

Combining the above derivation process, the solution of equation (12) is obtained:

According to the above function solution, it can be known that

Neutral belief investors who neither overestimate nor underestimate their decision-making ability can pay capital prices that are not frothy [6]. They are the equilibrium prices of the asset market. Then given any _{0} ≠ _{θ}_{θ}_{0} <

Arranged:

Simultaneous formulas (12) and (14), we have:

Because of 0 < _{θ}

So for any

Which in turn converts to:

From model (16) and model (17), it can be obtained that the assets in the case

Overconfident investors easily sway capital market pricing. They have a more significant say in capital market pricing. As a result, asset prices will be bid up when most investors in the market have overconfident beliefs [7]. This exceeds its actual equilibrium price and creates a market bubble. It causes volatility in capital market prices.

Continuing the asset price equation above, we build on Model (6) and Model (11). We use the variance value to describe the volatility of capital market prices:

Taking the partial derivative of the above function, we get:

From formula (18) and formula (19), it can be judged that the capital market price volatility is a decreasing function of investors’ overconfidence beliefs [8]. This means that the more optimistic investors are about capital markets, the more control they may have over capital pricing. The greater the volatility of asset prices, the more likely it will bring the risk of price fluctuations in the capital market.

Financial anomalies such as capital market price surges and sell-offs can be explained by investors’ heterogeneous beliefs and partial differential characteristics. Generally speaking, investors’ confidence in the capital market will bring a signal to the market that returns are expected [9]. This has contributed to the asset price being in a rising channel. As a result, it promotes the rise of the stock index and brings about the scene of individual stocks rising together. At this time, the investor is in a profitable state as a whole, and the prosperous state of the account will enhance the investor's confidence in investment decision-making. They are more willing to believe that they are “very insightful” and have more accurate and effective market information. Based on this belief, investors will further increase their investment in assets, eventually driving the capital market to rise sharply [10].

On the other hand, too pessimistic beliefs when the market is in a general downtrend channel will cause the market to sell. The “cut the meat out” strategy will become the norm. To this end, it is necessary to make reasonable use of and control investors’ heterogeneous beliefs and prevent the volatility risks brought by heterogeneous beliefs to the capital market to the greatest extent. For this, the following work needs to be done:

Standardize the capital market information disclosure system to reduce the mistransmission of investors’ heterogeneous beliefs to the capital market. At present, many listed companies are more inclined to disclose positive information rather than damaging information when disclosing information [11]. This is a detrimental approach to investors. This would be a big mistake for investors with overconfident beliefs. So we need to govern this behavior of listed companies. On the one hand, the securities regulatory authorities should start with the three primary regulatory goals of ensuring market fairness and transparency, protecting investors’ rights and interests, and reducing capital market risks. It strengthens the crackdown on the misreporting and omission of important information of listed companies to form a deterrent to securities crimes. On the other hand, maintain the collection and arrangement of listed companies’ market transactions and financial data. Strive to build a capital market information database and a dynamic supervision platform for the financial data of listed companies. The regulatory authorities implement classified management of listed companies’ information disclosure and focus on supervision of problem enterprises.

Strengthen the supervision of information disclosure and increase the “cost” of violations. Build a long-term mechanism to investigate and deal with false positives and omissions of important information. At the same time, the regulatory authorities intensified the punishment and gradually formed a regulatory deterrent and effective restraint on the information disclosure violations of listed companies [12]. At the same time, they need to improve the protection of the rights and interests of investors, continuously expand the scope of securities civil compensation litigation, and strengthen the free will of investors to exercise their right to sue.

Strengthen the intervention and supervision of inefficient markets. It can be seen from the above research that heterogeneous beliefs bring price fluctuations in the capital market. Therefore, as the maintainer of the market order, the government should take measures such as reducing speculation, limiting the daily price of the capital market, and setting up market transaction circuit breakers. In this way, the extreme, irrational behavior of the public can be reduced to reduce the risk of financial panic. Or the government builds the investor's investment utility framework by establishing a market economic climate index and an investor overconfidence index. This guides investors to recognize the cognitive biases and investment risks caused by heterogeneous beliefs. Ultimately, this leads investors to make sound investments.

In behavioral capital investment, heterogeneous belief refers to the psychological orientation that parties, including operators and investors, have different expectations for future capital returns, such as investor pessimism, overconfidence, and so on. We find that heterogeneous beliefs are an essential factor affecting capital market prices through the above model construction. Especially overconfidence beliefs. It has a substantial urging effect on the formation of capital market bubbles. Analysis of capital market price volatility from the capital pricing model under heterogeneous beliefs is a decreasing function of investors’ overconfidence beliefs. This shows that the more optimistic investors are about the capital market, the stronger their control over capital pricing and the greater the volatility of asset prices. Investor behavior is more likely to interfere with the price trend of the capital market and bring about the risk of price fluctuations in the capital market.

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