1. bookVolume 7 (2022): Edizione 1 (January 2022)
Dettagli della rivista
License
Formato
Rivista
eISSN
2444-8656
Prima pubblicazione
01 Jan 2016
Frequenza di pubblicazione
2 volte all'anno
Lingue
Inglese
access type Accesso libero

Differential equation model of financial market stability based on big data

Pubblicato online: 30 Dec 2021
Volume & Edizione: Volume 7 (2022) - Edizione 1 (January 2022)
Pagine: 711 - 718
Ricevuto: 17 Jun 2021
Accettato: 24 Sep 2021
Dettagli della rivista
License
Formato
Rivista
eISSN
2444-8656
Prima pubblicazione
01 Jan 2016
Frequenza di pubblicazione
2 volte all'anno
Lingue
Inglese
Abstract

The financial system is a complex, nonlinear chaotic dynamic system caused by its operating mechanism. Therefore, the application of previous forecasting models cannot explain the existence of various interference factors in the financial market and the chaotic characteristics of the financial system. With the help of financial market stability, the article establishes a series of differential equation models that reflect changes in interest rates in the financial system. The article introduces the factor of macro-control on the premise of respecting market regulation to regulate and intervene in economic relations and economic operation status. We apply the Logistic model and stability theory to analyse the positive equilibrium point characteristics of the system and obtain the interest rate liquidity equation with a time-lag financial network.

Keywords

MSC 2010

Introduction

Harmonious finance refers to an excellent financial, ecological environment in a region. The banking, securities, insurance and trust industries survive the survival of the fittest under the market mechanism and operate safely and orderly. The money market, capital market and insurance market promote each other. They develop in harmony with the economy, and various relationships are relatively harmonious [1]. Building a unified financial system is an integral part of building a harmonious society. In the 31 years of reform and opening up, Chinese financial industry has achieved considerable development. The financial market has initially established a multi-level financial system with relatively complete categories, flexible mechanisms and certain international competitiveness and conforming to the rules of the market economy. However, Chinese financial industry is still in the process of development, and there are still many imperfections and incoordinations. The mechanism for harmonious development among financial market entities such as banks, credit reporting companies and guarantee companies is incomplete. The cooperative relationship between Chinese banks and foreign banks is not yet sound. Interest disputes between various subjects continue. This unbalanced financial institution directly affects the efficiency of resource allocation in the financial market, and at the same time, reduces the risk prevention capability of the financial industry and hinders the goal of building harmonious finance.

Banks, non-bank financial institutions, bank intermediaries and other entities cooperate and complement each other in an efficient and harmonious financial ecosystem and live in harmony to form a financial symbiosis network. Harmonious symbiosis among various financial entities contributes to the balance of financial ecology, and they promote the sustainable development of the entire economic system [2]. Aiming at the shortcomings of existing research, this article draws on the theory of biological symbiosis to study the formation mechanism of financial symbiosis and the type of symbiosis. At the same time, we use the Logistic model to construct the partial benefit symbiosis and reciprocity symbiosis model of financial symbiosis. The article analyses the stability of the symbiotic relationship and proposes countermeasures and suggestions for developing the symbiotic financial relationship.

The formation mechanism and type division of financial symbiosis
The formation mechanism of financial symbiosis

In a specific economic environment, legal environment, credit environment, market environment and institutional environment, financial market entities provide financial services based on their interests and behaviours [3]. There are shared interests and survival foundations among all market entities. They participate in the market game while carrying out mutually beneficial cooperation to form a symbiosis and coexistence relationship. For example, guarantee companies provide banks with intermediary services such as verification, notarisation, evaluation, coordination and arbitration in market competition, transaction order and dispute resolution as a third party, but also require banks to provide customer credit information for their services. They and commercial banks are mutually beneficial, and they cannot survive after separation. As a result, a symbiotic coexistence relationship is formed.

The foundation of the symbiotic relationship between the financial market entities lies in a symbiotic matrix between each one and the others. They are mainly complementary resources among financial market entities. To promote the smooth development of symbiosis activities, financial market entities need to develop symbiosis communication methods and mechanisms, such as establishing regular meetings, mutual visits and other communication mechanisms and methods [4]. We can call these communication mechanisms and methods a symbiotic interface. The efficiency and function of the symbiosis interface are the key factors that determine the efficiency of financial symbiosis and the stability of the symbiosis relationship.

Symbiosis energy is a concrete manifestation of the viability and value-added ability of financial symbiosis. In the financial symbiosis relationship, the symbiosis energy mainly refers to the funds provided by the bank to the financial market entities [5]. The business development, the improvement of management ability, the enhancement of the ability to resist risks, and net profit increase. The characteristic value of the symbiosis interface and the degree of symbiosis are two key variables that affect the energy of the symbiosis. The characteristic value of the symbiosis interface is an important parameter to measure the communication resistance on the symbiosis interface. The more symbiotic the interfaces, the larger the contact surface and the better the contact medium, the smaller the communication resistance, and the closer the corresponding characteristic value is to zero. In addition, the greater the degree of symbiosis, the greater the energy of symbiosis. The level of symbiotic energy is the prerequisite for the continuous development of symbiotic relationships.

Types of financial symbiosis

According to the differences in the energy distribution of financial market entities, we divide the financial symbiosis relationship into two types: favour symbiosis and mutual symbiosis. The symbiosis of partial benefit has the following characteristics: (1) New energy is produced, but one party obtains most of the new energy. (2) The symbiotic relationship is beneficial to one party but not harmful to the other party. (3) There are bilateral two-way exchanges between financial market entities. The reciprocal symbiosis relationship has the following characteristics: (1) New energy is generated, and there is a broad-spectrum distribution of new energy. (2) There is a bilateral exchange mechanism and a multilateral exchange mechanism between the financial market entities. (3) The growth and evolution of financial market entities are synchronised. Figure 1 shows the financial symbiosis relationship.

Fig. 1

Financial symbiosis

Model construction of financial symbiosis

The harmony and stability of the financial symbiosis relationship are essential for establishing a unified financial system [6]. This article will first construct a model of the financial symbiosis relationship to accurately portray the financial symbiosis relationship and the stable conditions of the financial symbiosis relationship.

Model assumptions

(1) The profits of financial market entities can reflect the endogenous and exogenous changes experienced by various financial market entities in the evolution of financial symbiosis. We may explain the evolution process of the symbiosis relationship by describing the profit changes of the main body of the financial market. (2) The profit x of financial market entities is a function of time t. (3) The growth of financial market entities is constrained by various factors of production. In a given time and geographical space, the total production factors such as technology, raw materials, labour and capital are certain. We assume that the maximum amount is N. As the main body of the financial market grows, the economic benefits brought by its scale will rise to a certain level. It will inevitably be restricted by factor endowments and enter a critical stage. Therefore, the main body of the financial market has the most significant quantity of production factors N. When x = N, the main body of the financial market stops growing. (4) The growth rate r of financial market entities decreases with the increase of their production factors. With the growth of the main body of the financial market, the factors of production that they can take are getting less and less, and the growth is slowing down. While the main body of the financial market grows, other market central bodies’ technological innovation, key resource acquisition, differentiated marketing and other business behaviours will inhibit the growth of the main body of the financial market. (5) Each additional unit of production factors of the main body of the financial market will have a 1/N inhibitory effect on the growth of itself and other market-main bodies.

The main body of the financial market uses the 1/N factor of production for every additional unit of production factor and increases x units of production factor of x/N. Then the ‘surplus production factor’ that financial market entities can obtain is only (1xN) \left( {1 - {x \over N}} \right) . Taking into account the continuity of the growth of financial market entities, we can establish the profit change equation of financial symbiosis through the differential method dxdt=rx(1xN) {{dx} \over {dt}} = rx\left( {1 - {x \over N}} \right)

Partial interest symbiosis model of financial symbiosis

In the symbiosis of partial benefits, we call the main body of the financial market that benefits more as the leader and the other party as the dependent. We denote the profit scale of the leader as x1(t) and the profit scale of the dependents as x2(t). The dominant person can develop on his own before the dependent person appears. At this time, its profit satisfies the Logistic model: dx1dt=r1x1(1x1N1) {{d{x_1}} \over {dt}} = {r_1}{x_1}\left( {1 - {{{x_1}} \over {{N_1}}}} \right) N1 is the amount of production factors taken by the leader. According to the hypothesis of this article, the profit level of the leader can be described as dx1dt=r1x1(1x1N1+ax1N1),a>0 {{d{x_1}} \over {dt}} = {r_1}{x_1}\left( {1 - {{{x_1}} \over {{N_1}}} + {{a{x_1}} \over {{N_1}}}} \right),\quad a > 0 α is the contribution of each unit leader's natural market size saturation to the leader's profit level. We count the natural negative growth rate of the dependant's profit level as r2. In a market structure where only the dependants exist alone, we can describe the profit level of the dependants as dx2dt=r2x2 {{d{x_2}} \over {dt}} = - {r_2}{x_2} . After the leader is introduced into the market, the profit level of the dependents will increase [7]. The profit level of the dependant can be further described as dx2dt=r2x2(1βx1N1),β>0 {{d{x_2}} \over {dt}} = {r_2}{x_2}\left( { - 1 - {{\beta {x_1}} \over {{N_1}}}} \right),\quad \beta > 0 β is the contribution of the natural market size saturation of the dominant per unit to the profit level of the dependents. The saturation of the ideal market size of the dependents has a hindering effect on their profit levels [8]; therefore, the behaviour of the dependant can ultimately be described as dx2dt=r2x2(1βx1N1x2N2) {{d{x_2}} \over {dt}} = {r_2}{x_2}\left( { - 1 - {{\beta {x_1}} \over {{N_1}}} - {{{x_2}} \over {{N_2}}}} \right) From this, we can infer the partial benefit symbiosis model of financial symbiosis to be the following: dx1dt=r1x1(1x1N1+ax2N1)dx2dt=r2x2(1+βx1N1x2N2)} \left. {\matrix{ \hfill{{{d{x_1}} \over {dt}} = {r_1}{x_1}\left( {1 - {{{x_1}} \over {{N_1}}} + {{a{x_2}} \over {{N_1}}}} \right)} \cr \hfill{{{d{x_2}} \over {dt}} = {r_2}{x_2}\left( { - 1 + {{\beta {x_1}} \over {{N_1}}} - {{{x_2}} \over {{N_2}}}} \right)} \cr } } \right\}

Reciprocal symbiosis model of financial symbiosis

Before the two financial market entities formed a symbiosis, their profit level satisfies the Logistic model: dx1dt=r1x1(1x1N1)dx2dt=r2x2(1x2N2)} \left. {\matrix{\hfill {{{d{x_1}} \over {dt}} = {r_1}{x_1}\left( {1 - {{{x_1}} \over {{N_1}}}} \right)} \cr \hfill {{{d{x_2}} \over {dt}} = {r_2}{x_2}\left( {1 - {{{x_2}} \over {{N_2}}}} \right)} \cr } } \right\} x1(t) and x2(t) are the profit levels of financial market entities 1 and 2, respectively. When the main body of the financial market 1 and that of the financial market 2 coexist, the formation of the symbiotic relationship can promote the profit level of both parties [9]. Therefore, the description of the profit level of financial market entities 1 and 2 should be changed to the mutually beneficial symbiosis model in financial symbiosis, as follows: dx1(t)dt=r1x1(1x1N1+δ1x2N2)dx1(t)dt=r1x1(1x1N1+δ2x2N2)} \left. {\matrix{\hfill {{{d{x_1}(t)} \over {dt}} = {r_1}{x_1}\left( {1 - {{{x_1}} \over {{N_1}}} + {{{\delta _1}{x_2}} \over {{N_2}}}} \right)} \cr \hfill {{{d{x_1}(t)} \over {dt}} = {r_1}{x_1}\left( {1 - {{{x_1}} \over {{N_1}}} + {{{\delta _2}{x_2}} \over {{N_2}}}} \right)} \cr } } \right\} δ1 > 0, δ2 > 0, δ1 is the contribution of the profit level of the financial market entity 1 unit to the profit level of the financial market entity 2. δ2 represents the contribution of the profit level of the financial market entity 2 to the profit level of the financial market entity 1.

Stability analysis of financial symbiosis model
Stability analysis of the favoured symbiosis model

Now we use differential equations to solve the stability of the partial benefit symbiosis model. f(x1,x2)dx1dt=r1,r1(1x1N1+δ1x2N1)=0g(x1,x2)dx2dt=r2,r2(1+δ1x1N1x2N2)=0} \left. {\matrix{ \hfill {f({x_1},{x_2}) \equiv {{d{x_1}} \over {dt}} = {r_1},\quad {r_1}\left( {1 - {{{x_1}} \over {{N_1}}} + {{{\delta _1}{x_2}} \over {{N_1}}}} \right) = 0}\cr \hfill {g({x_1},{x_2}) \equiv {{d{x_2}} \over {dt}} = {r_2},\quad {r_2}\left( { - 1 + {{{\delta _1}{x_1}} \over {{N_1}}} - {{{x_2}} \over {{N_2}}}} \right) = 0} \cr } } \right\} The equilibrium point P1(N,0), P2(N1(1δ1)1δ1δ2,N3(δ21)1δ1δ2) {P_2}\left( {{{{N_1}(1 - {\delta _1})} \over {1 - {\delta _1}{\delta _2}}},{{{N_3}({\delta _2} - 1)} \over {1 - {\delta _1}{\delta _2}}}} \right) , P3(0,0) can be obtained by solving the differential equation. We analyse the stability of the above three equilibrium points and find that point P3 is an unstable point under any conditions. For the balance point P2 to have practical meaning, it needs to be located in the I quadrant (x1,x2 ≥ 0) of the phase plane, and one of the following two conditions must be met: δ1<1,δ2>1δ1δ2<1 {\delta _1} < 1,\quad {\delta _2} > 1\quad {\delta _1}{\delta _2} < 1 δ1>1,δ2<1δ1δ2>1 {\delta _1} > 1,\quad {\delta _2} < 1\quad {\delta _1}{\delta _2} > 1 We can judge the stability of the equilibrium point according to the direct method. The first-order Taylor expansion of the differential equation can be performed at the equilibrium point x1*, x2* to obtain dx1dt=r1(1+δ1x2N22x1N1)(x1x1*)+r1x1δ1(x2x2*)N2dx2dt=r2x2δ2(x1x1*)N1+r2(δ2x1N112x2N2)(x2x2*)} \left. {\matrix{ \hfill {{{d{x_1}} \over {dt}} = {r_1}\left( {1 + {{{\delta _1}{x_2}} \over {{N_2}}} - {{2{x_1}} \over {{N_1}}}} \right)\left( {{x_1} - {x_1}^*} \right) + {r_1}{x_1}{{{\delta _1}({x_2} - {x_2}^*)} \over {{N_2}}}} \cr \hfill {{{d{x_2}} \over {dt}} = {{{r_2}{x_2}{\delta _2}({x_1} - {x_1}^*)} \over {{N_1}}} + {r_2}\left( {{{{\delta _2}{x_1}} \over {{N_1}}} - 1 - {{2{x_2}} \over {{N_2}}}} \right)\left( {{x_2} - {x_2}^*} \right)}\cr } } \right\} Then the coefficient matrix A can be denoted as A=(r1(1+δ1x2N22x1N1)r1x1δ1r1x2δ2N1r2(δ2x2N112x2N2)) A = \left( {\matrix{ {{r_1}\left( {1 + {{{\delta _1}{x_2}} \over {{N_2}}} - {{2{x_1}} \over {{N_1}}}} \right)} & {{r_1}{x_1}{\delta _1}} \cr {{{{r_1}{x_2}{\delta _2}} \over {{N_1}}}} & {{r_2}\left( {{{{\delta _2}{x_2}} \over {{N_1}}} - 1 - {{2{x_2}} \over {{N_2}}}} \right)} \cr } } \right) . We substitute the equilibrium point P2(N1(1δ1)1δ1δ2,N2(δ11)1δ1δ2) {P_2}\left( {{{{N_1}(1 - {\delta _1})} \over {1 - {\delta _1}{\delta _2}}},{{{N_2}({\delta _1} - 1)} \over {1 - {\delta _1}{\delta _2}}}} \right) into the coefficient matrix A. According to the method of determining the stable point of the differential equation, the conditions for obtaining the stable node of the model are: δ1<1δ2>1δ1δ2<1 {\delta _1} < 1\quad {\delta _2} > 1\quad {\delta _1}{\delta _2} < 1 Three conditions must be met to achieve a stable symbiosis of partial interest among the financial market entities: (1) δ1 < 1 means that the dependent person's contribution to the leader's profit is relatively small. (2) δ2 > 1 means that the dominant player makes a relatively significant contribution to the profits of the dependents. (3) δ1δ2 < 1 means that when two financial market entities reach a stable state of symbiosis with partial benefits, δ1 is required to be small and δ2 is large [10]. This requires a larger scale of the leader. When the favoured symbiosis reaches a stable state, the symbiosis energy obtained by the dependent is N1(1δ1)1δ1δ2,N1(1δ1)1δ1δ2>N1 {{{N_1}(1 - {\delta _1})} \over {1 - {\delta _1}{\delta _2}}},{{{N_1}(1 - {\delta _1})} \over {1 - {\delta _1}{\delta _2}}} > {N_1} . The symbiotic energy obtained by the dominant player is N2(δ21)1δ1δ2,N2(δ21)1δ1δ2>N2 {{{N_2}({\delta _2} - 1)} \over {1 - {\delta _1}{\delta _2}}},{{{N_2}({\delta _2} - 1)} \over {1 - {\delta _1}{\delta _2}}} > {N_2} .

Stability analysis of the reciprocal symbiosis model

Differential equations solve the stability of the reciprocal symbiosis model. f(x1,x2)dx1dt=r1x1(1x1N1+δ1x2N1)=0g(x1,x2)dx2dt=r2x2(1x2N2+δ2x2N1)=0} \left. {\matrix{ {f({x_1},{x_2}) \equiv {{d{x_1}} \over {dt}} = {r_1}{x_1}\left( {1 - {{{x_1}} \over {{N_1}}} + {{{\delta _1}{x_2}} \over {{N_1}}}} \right) = 0} \hfill \cr {g({x_1},{x_2}) \equiv {{d{x_2}} \over {dt}} = {r_2}{x_2}\left( {1 - {{{x_2}} \over {{N_2}}} + {{{\delta _2}{x_2}} \over {{N_1}}}} \right) = 0} \hfill \cr } } \right\} The equilibrium point P(x1,x2)=(N1(1+δ1)1δ1δ2,N2(1+δ2)1δ1δ2) P({x_1},{x_2}) = \left( {{N_1}{{(1 + {\delta _1})} \over {1 - {\delta _1}{\delta _2}}},{N_2}{{(1 + {\delta _2})} \over {1 - {\delta _1}{\delta _2}}}} \right) , can be obtained by solving the differential equation. When x1 > 0, x2 > 0, N1(1+δ1)1δ1δ2>0 {N_1}{{(1 + {\delta _1})} \over {1 - {\delta _1}{\delta _2}}} > 0 , N2(1+δ2)1δ1δ2>0 {N_2}{{(1 + {\delta _2})} \over {1 - {\delta _1}{\delta _2}}} > 0 it means that the two financial market entities reciprocally coexist. Therefore, a condition for the mutual symbiosis of the two financial market entities is δ1δ2 < 1.

We carry out the first-order Taylor expansion of the differential equations to get dx1dt=r1(12x1N1+δ2x2N2(x1x1*))+r1x1δ1(x2x2*)N2dx2dt=(r2x2δ2N1)(x1x1*)+r2(12x2N2+δ2x1N1)(x2x2*)} \left. {\matrix{ \hfill {{{d{x_1}} \over {dt}} = {r_1}\left( {1 - {{2{x_1}} \over {{N_1}}} + {{{\delta _2}{x_2}} \over {{N_2}}}({x_1} - {x_1}^*)} \right) + {r_1}{x_1}{{{\delta _1}({x_2} - {x_2}^*)} \over {{N_2}}}} \cr \hfill {{{d{x_2}} \over {dt}} = \left( {{{{r_2}{x_2}{\delta _2}} \over {{N_1}}}} \right)({x_1} - {x_1}^*) + {r_2}\left( {1 - {{2{x_2}} \over {{N_2}}} + {{{\delta _2}{x_1}} \over {{N_1}}}} \right)({x_2} - {x_2}^*)} \cr } } \right\} We substitute P(x1x2)=(N1(1δ1)1δ1δ2,N2(1+δ2)1δ1δ2) P({x_1}{x_2}) = \left( {{N_1}{{(1 - {\delta _1})} \over {1 - {\delta _1}{\delta _2}}},{N_2}{{(1 + {\delta _2})} \over {1 - {\delta _1}{\delta _2}}}} \right) into Eq. (15), and the relative system matrix is A=(r1(1δ1)1δ1δ2r1x1δ1(1+δ1)N2(1δ1δ2)N2r2δ2(1+δ2)N1(1δ1δ2)r2(1δ2)1δ1δ2) A = \left( {\matrix{ {{{{r_1}( - 1 - {\delta _1})} \over {1 - {\delta _1}{\delta _2}}}} & {{{{r_1}{x_1}{\delta _1}(1 + {\delta _1})} \over {{N_2}(1 - {\delta _1}{\delta _2})}}} \cr {{{{N_2}{r_2}{\delta _2}(1 + {\delta _2})} \over {{N_1}(1 - {\delta _1}{\delta _2})}}} & {{{{r_2}( - 1 - {\delta _2})} \over {1 - {\delta _1}{\delta _2}}}} \cr } } \right) According to the stability theory of differential equations, we find that the condition for a stable point to be a stable node is δ1δ2 < 1. Therefore, to achieve a stable symbiosis, the symbiosis relationship in the mutually beneficial symbiosis model is δ1δ2 < 1. Considering the symmetry of financial market entities, we can further determine the stable symbiosis condition δ1 < 1,δ2 < 1.

The two conditions that need to be met to achieve a stable reciprocal symbiosis relationship can be explained δ1 < 1, δ2 < 1. indicates that the two financial market entities in a mutually beneficial symbiosis relationship contribute relatively little to each other's output. When the reciprocal symbiosis reaches a stable state, the symbiosis energy obtained by the financial market entity 1 is N1(1+δ1)1δ1δ2,N1(1+δ1)1δ1δ2>N1 {N_1}{{(1 + {\delta _1})} \over {1 - {\delta _1}{\delta _2}}},{N_1}{{(1 + {\delta _1})} \over {1 - {\delta _1}{\delta _2}}} > {N_1} , whereas the symbiotic energy obtained by the financial market entity 2 is N2(1+δ2)1δ1δ2,N2(1+δ2)1δ1δ2>N2 {N_2}{{(1 + {\delta _2})} \over {1 - {\delta _1}{\delta _2}}},{N_2}{{(1 + {\delta _2})} \over {1 - {\delta _1}{\delta _2}}} > {N_2} .

Countermeasures for the stable and harmonious development of financial symbiosis

In the early stage of financial market opening, due to the Chinese government's policy restrictions on sole proprietorship, foreign financial institutions depended on the legal status of local financial institutions. They need to export a large amount of technology and management experience to local financial institutions. However, the investment of Chinese banks is mostly substitutable. Imitable resources such as business, branches and financial policies, and a symbiotic relationship of partial benefit, has been formed between Chinese and foreign financial institutions. With the gradual liberalisation of Chinese financial market policies, the dependence of foreign financial institutions on the legal status of local financial institutions will gradually decrease [11]. Local financial institutions still rely on foreign financial institutions due to their learning ability and other problems, and so foreign financial institutions require greater control over the symbiotic relationship. This has led to unstable phenomena such as equity changes and mergers and acquisitions.

Financial market entities should cultivate and enhance their core capabilities and reduce their dependence on other financial market entities. As far as Chinese banks are concerned, the following measures can be undertaken:

Form irreplaceable valuable resources and capabilities.

Grasp the advanced management concepts and business models of foreign banks as soon as possible. Only in this way can they become the dominant player in the symbiosis with foreign banks.

The government should strive to improve the financial symbiosis environment and promote the growth of domestic weak financial market entities to achieve the goal of the harmonious development of various financial market entities.

China should speed up establishing a sound credit reporting system, cultivate traditional rating agencies and strengthen the supervision of the credit reporting industry. It is also necessary to promote the establishment of a credit investigation system for small and medium-sized enterprises, and formulate laws and regulations applicable to national credit investigation. China needs to quickly establish a unified management agency for the credit reporting system. In addition, the establishment of a credit guarantee legal system should be accelerated, with regard to the access and exit system of guarantee institutions, capital injection and compensation systems, business scope and operating procedures, risk control and financial systems, industry self-discipline and rights protection systems, government coordination and supervision, etc. Make regulations. In terms of guarantee agencies, China should establish a credit rating system for credit guarantee agencies as soon as possible. The local government will contact a third-party evaluation agency to establish a unified credit rating system approved by the bank for the guarantee agency. We need to find and recommend a group of good guarantee agencies to focus on.

Conclusion

Based on the previous analysis of the stability of the financial symbiosis, partial benefit symbiosis and reciprocity symbiosis model, the author found the following rules. Factors such as the resources, capabilities and scale of financial market entities determine their bargaining power in symbiotic behaviour. The distribution of symbiosis energy needs to match the bargaining power among financial market entities. Such a symbiotic relationship will be stable. Therefore, in the short term, the stability of the symbiotic relationship is determined by whether the bargaining power between the financial market entities matches the symbiotic energy distribution. However, in unequal bargaining power, financial solid market entities are prone to opportunistic behaviour and tend to use coercion, punishment and other means. Weak financial market entities tend to increase their bargaining power.

Fig. 1

Financial symbiosis
Financial symbiosis

Lu, Z., Yan, H., & Zhu, Y. European option pricing model based on uncertain fractional differential equation. Fuzzy Optimization and Decision Making., 2019; 18(2): 199–217. LuZ. YanH. ZhuY. European option pricing model based on uncertain fractional differential equation Fuzzy Optimization and Decision Making 2019 18 2 199 217 10.1007/s10700-018-9293-4 Search in Google Scholar

Bocquet, M., Brajard, J., Carrassi, A., & Bertino, L. Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models. Nonlinear Processes in Geophysics., 2019; 26(3): 143–162. BocquetM. BrajardJ. CarrassiA. BertinoL. Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models Nonlinear Processes in Geophysics 2019 26 3 143 162 10.5194/npg-26-143-2019 Search in Google Scholar

Liang, P. J., & Zhang, G. On the social value of accounting objectivity in financial stability. The Accounting Review., 2019; 94(1): 229–248. LiangP. J. ZhangG. On the social value of accounting objectivity in financial stability The Accounting Review 2019 94 1 229 248 10.2308/accr-52108 Search in Google Scholar

Liu, X., Sun, H., Zhang, Y., & Fu, Z. A scale-dependent finite difference approximation for time fractional differential equation. Computational Mechanics., 2019; 63(3): 429–442. LiuX. SunH. ZhangY. FuZ. A scale-dependent finite difference approximation for time fractional differential equation Computational Mechanics 2019 63 3 429 442 10.1007/s00466-018-1601-x Search in Google Scholar

Golbabai, A., Nikan, O., & Nikazad, T. Numerical analysis of time fractional Black–Scholes European option pricing model arising in financial market. Computational and Applied Mathematics., 2019; 38(4): 1–24. GolbabaiA. NikanO. NikazadT. Numerical analysis of time fractional Black–Scholes European option pricing model arising in financial market Computational and Applied Mathematics 2019 38 4 1 24 10.1007/s40314-019-0957-7 Search in Google Scholar

Cai, S., Cai, Y., & Mao, X. A stochastic differential equation SIS epidemic model with two independent Brownian motions. Journal of Mathematical Analysis and Applications., 2019; 474(2): 1536–1550. CaiS. CaiY. MaoX. A stochastic differential equation SIS epidemic model with two independent Brownian motions Journal of Mathematical Analysis and Applications 2019 474 2 1536 1550 10.1016/j.jmaa.2019.02.039 Search in Google Scholar

Zhang, Q., & Li, T. Asymptotic stability of compact and linear θ-Methods for space fractional delay generalized diffusion equation. Journal of Scientific Computing., 2019; 81(3): 2413–2446. ZhangQ. LiT. Asymptotic stability of compact and linear θ-Methods for space fractional delay generalized diffusion equation Journal of Scientific Computing 2019 81 3 2413 2446 10.1007/s10915-019-01091-1 Search in Google Scholar

Hu, X., Li, J. & Aram, Research on style control in planning and designing small towns. Applied Mathematics and Nonlinear Sciences., 2020; 6(1): 57–64. HuX. LiJ. Aram Research on style control in planning and designing small towns Applied Mathematics and Nonlinear Sciences 2020 6 1 57 64 10.2478/amns.2020.2.00077 Search in Google Scholar

Aidara, S. Anticipated backward doubly stochastic differential equations with non-Liphschitz coefficients. Applied Mathematics and Nonlinear Sciences., 2019; 4(1): 9–20. AidaraS. Anticipated backward doubly stochastic differential equations with non-Liphschitz coefficients Applied Mathematics and Nonlinear Sciences 2019 4 1 9 20 10.2478/AMNS.2019.1.00002 Search in Google Scholar

Wang, W., Chen, Y., & Fang, H. On the variable two-step IMEX BDF method for parabolic integro-differential equations with nonsmooth initial data arising in finance. SIAM Journal on Numerical Analysis., 2019; 57(3): 1289–1317. WangW. ChenY. FangH. On the variable two-step IMEX BDF method for parabolic integro-differential equations with nonsmooth initial data arising in finance SIAM Journal on Numerical Analysis 2019 57 3 1289 1317 10.1137/18M1194328 Search in Google Scholar

Yao, K., & Liu, B. Parameter estimation in uncertain differential equations. Fuzzy Optimization and Decision Making., 2020; 19(1): 1–12. YaoK. LiuB. Parameter estimation in uncertain differential equations Fuzzy Optimization and Decision Making 2020 19 1 1 12 10.1007/s10700-019-09310-y Search in Google Scholar

Articoli consigliati da Trend MD

Pianifica la tua conferenza remota con Sciendo