International journal of financial engineering, Mar 1, 2019
The purpose of this paper is to discuss the general risk assessment under the Hologram framework ... more The purpose of this paper is to discuss the general risk assessment under the Hologram framework for the enterprise based on big data language; and to illustrate the Hologram as a new tool for establishing a mechanism to evaluate SMEs growth and change in financial technology dynamically (here we mainly focus on SMEs as they are one of the very important classes for enterprises with less information available from financial accounting report and associated assets. Indeed, the approach discussed here is applicable to general enterprises).The key idea of our new approach is to introduce and use the “Hologram” (similar to, “holographic portrait” used in portrait holography), a platform for data fusion dynamically, as a tool and mechanism to describe the dynamic evolution of SMEs based on their business dynamic behavior. Through processing structured and/or unstructured data in terms of “related-party” information sets which analyze (1) “investment” and (2) “management” information provided by SMEs’ business behavior, and extracting “Risk Genes” from complex financial network structures in the business ecosystem, we can establish a “good” or “bad” rating for SMEs by using data fusion dynamically and financial technology. This method to assess SMEs is a new approach to evaluating SMEs’ development dynamically based on the network structure information of enterprise and business behavior. The framework introduced in this paper for the dynamic mechanism of SMEs’ development and evolution allows us to assess the risk of any SMEs (in particular to evaluate SMEs’ loan applications) even not available for critical data required in traditional finance analysis including information such as financial accounting and associated assets, etc. This new “Hologram” approach for SMEs assessment is a pioneering innovation that incorporates big data and financial technology for inclusive financial services in practical application. Ultimately, the Hologram approach offers a new theoretical solution for the long-standing problem of credit risk assessment for SMEs and individuals in practice.Since the information embedded in SMEs’ business behavior reveals the competition and cooperation mechanism that drives its stochastic resonance (SR) behavior which is associated with successful SMEs development, the two concepts of SAI and URR under the Hologram approach to risk assessment that identifies if an SME is “good” are based on the network generated from an SMEs’ related-party information in terms of “investment” and “management” dynamically, along with other available information such as related investment capital and risk control. Significantly, the Hologram approach to risk assessment for SMEs does not require critical data of traditional financial account and related assets, etc. which heavily depend on financial accounting and associated assets used by financial risk analysis in practice. Using big data and FinTech Hologram method discussed in this paper utilizes the related-party information (in term of investment and management) of each SME which exists in an embedded business network to overcome the situation for SMEs which always have not or have not enough in providing accounting and associated asset information in the practice.By the feature of each Hologram for a given SME, one always has the related-party information in terms of either investment, or management dynamically, which is indeed also an explanation for the reason why the new approach proposed only comes true only until the era of big data’s occurring by using ideas from financial technology today.Furthermore, this paper explores the implementation of the “Holo Credit Loan”, a pure credit loan without any collateral and guarantee launched in 2016, as practical applications of the Hologram approach. We illustrate the framework of SMEs risk assessment under the Holograms new theoretical basis for solving the long-standing problem of credit risk assessment for SMEs (and individuals). Moreover, this paper’ conclusion will address the performance of the “Holo Credit Loan”.
introduced the notion of $L^0$--convex compactness for an $L^0$--convex subset of a Hausdorff top... more introduced the notion of $L^0$--convex compactness for an $L^0$--convex subset of a Hausdorff topological module over the topological algebra $L^0(\mathcal{F},K)$, where $K$ is the scalar field of real or complex numbers and $L^0(\mathcal{F},K)$ the algebra of equivalence classes of $K$--valued measurable functions defined on a $\sigma$--finite measure space $(\Omega,\mathcal{F},\mu)$, endowed with the topology of convergence locally in measure. A complete random normed module $($briefly, $RN$ module$)$, as a random generalization of a Banach space, is just such a kind of topological module, this paper further introduces the notion of random normal structure and gives various kinds of determination theorems for a closed $L^0$--convex subset to have random normal structure or $L^0$--convex compactness, in particular we prove a characterization theorem for a closed $L^0$--convex subset to have $L^0$--convex compactness, which can be regarded as a generalization of the famous James characterization theorem for a closed convex subset of a Banach space to be weakly compact. Based on these preparations, we generalize the classical Kirk's fixed point theorem from a Banach space to a complete $RN$ module as follows: Let $(E,\|\cdot\|)$ be a complete $RN$ module and $V \subset E$ a nonempty $L^0$--convexly compact closed $L^0$--convex subset with random normal structure, then every nonexpansive self--mapping $f$ from $V$ to $V$ has a fixed point in $V$. The generalized Kirk's fixed point theorem is also of fundamental importance in random functional analysis, for example, we can derive from it a very general random fixed point theorem, which unifies and improves several known random fixed point theorems for random nonexpansive mappings.
The goal of this paper is to develop some fundamental and important nonlinear analysis for single... more The goal of this paper is to develop some fundamental and important nonlinear analysis for single-valued mappings under the framework of p-vector spaces, in particular, for locally p-convex spaces for 0 < p ≤ 1. More precisely, based on the fixed point theorem of single-valued continuous condensing mapping in locally p-convex spaces as the starting point, we first establish best approximation results for (single-valued) continuous condensing mappings which are then used to develop new results for three classes of nonlinear mappings consisting of 1) condensing; 2) 1-set contractive; and 3) semiclosed 1-set contractive mappings in locally p-convex spaces. Next they are used to establish general principle for nonlinear alternative, Leray - Schauder alternative, fixed points for non-self mappings with different boundary conditions for nonlinear mappings from locally p-convex spaces, to nonexpansive mappings in uniformly convex Banach spaces, or locally convex spaces with Opial condit...
The goal of this paper is to establish a general fixed point theorem for upper semicontinuous set... more The goal of this paper is to establish a general fixed point theorem for upper semicontinuous set-values mappings in p-vector spaces (p∈(0, 1]), which include topological vector spaces as a special class. These new results provide an answer to Schauder conjecture in the affirmative under the setting of p-vector spaces for set-valued mappings, which would be fundamental for nonlinear functional analysis in mathematics. AMS Classification: 47H04, 47H10, 46A16, 46A55, 49J27, 49J35, 52A07, 54C60, 54H25, 55M20
International Journal of Intelligent Systems, Apr 6, 2021
The purpose of this paper is to establish a generalized dynamical framework for small and micro‐e... more The purpose of this paper is to establish a generalized dynamical framework for small and micro‐enterprise (SME) growth in the tech‐economic paradigm, and develop a novel quantitative method for the decision‐making of optimal equity and capital structure under the measurement of dynamical risk profiles. Based on the numerical simulations in different scenarios, we systematically study the dependence of SME growth performance on various factors, including capital structure, investment preference, and internal risk level, and find that dynamical optimal equity structure always corresponds to the better performance on value at response risks, and significantly reduces the bilateral cooperative risk at the inconspicuous cost of systematic response risk. Moreover, it is also observed that SME state behaves some important nonmonotonous features, such as stochastic resonance with internal risk level, generalized stochastic resonance with operating capital leverage. These results will provide the latent support for SMEs to create useful decision rules in capital optimization, risk management, and growth path regulation.
Communications in computer and information science, 2019
The goal of this paper is to introduce a new notion called “Consensus Game (CG)” with motivation ... more The goal of this paper is to introduce a new notion called “Consensus Game (CG)” with motivation from the mechanism design of blockchain economy under the consensus incentives from Bitcoin ecosystems in financial technology (Fintech), we then establish the general existence results for consensus equilibria of consensus games in terms of corresponding interpretation based on the viewpoint of Blockchain consensus in Fintech by applying the concept of hybrid solutions in game theory. As applications, our discussion in this paper for the illustration of some issues and problems on the stability of mining pool-games for miners by applying consensus games shows that the concept of consensus equilibria could be used as a fundamental tool for the study of consensus economics under the framework of Blockchain economy in Fintech.
International journal of financial engineering, Mar 1, 2019
The purpose of this paper is to discuss the general risk assessment under the Hologram framework ... more The purpose of this paper is to discuss the general risk assessment under the Hologram framework for the enterprise based on big data language; and to illustrate the Hologram as a new tool for establishing a mechanism to evaluate SMEs growth and change in financial technology dynamically (here we mainly focus on SMEs as they are one of the very important classes for enterprises with less information available from financial accounting report and associated assets. Indeed, the approach discussed here is applicable to general enterprises).The key idea of our new approach is to introduce and use the “Hologram” (similar to, “holographic portrait” used in portrait holography), a platform for data fusion dynamically, as a tool and mechanism to describe the dynamic evolution of SMEs based on their business dynamic behavior. Through processing structured and/or unstructured data in terms of “related-party” information sets which analyze (1) “investment” and (2) “management” information provided by SMEs’ business behavior, and extracting “Risk Genes” from complex financial network structures in the business ecosystem, we can establish a “good” or “bad” rating for SMEs by using data fusion dynamically and financial technology. This method to assess SMEs is a new approach to evaluating SMEs’ development dynamically based on the network structure information of enterprise and business behavior. The framework introduced in this paper for the dynamic mechanism of SMEs’ development and evolution allows us to assess the risk of any SMEs (in particular to evaluate SMEs’ loan applications) even not available for critical data required in traditional finance analysis including information such as financial accounting and associated assets, etc. This new “Hologram” approach for SMEs assessment is a pioneering innovation that incorporates big data and financial technology for inclusive financial services in practical application. Ultimately, the Hologram approach offers a new theoretical solution for the long-standing problem of credit risk assessment for SMEs and individuals in practice.Since the information embedded in SMEs’ business behavior reveals the competition and cooperation mechanism that drives its stochastic resonance (SR) behavior which is associated with successful SMEs development, the two concepts of SAI and URR under the Hologram approach to risk assessment that identifies if an SME is “good” are based on the network generated from an SMEs’ related-party information in terms of “investment” and “management” dynamically, along with other available information such as related investment capital and risk control. Significantly, the Hologram approach to risk assessment for SMEs does not require critical data of traditional financial account and related assets, etc. which heavily depend on financial accounting and associated assets used by financial risk analysis in practice. Using big data and FinTech Hologram method discussed in this paper utilizes the related-party information (in term of investment and management) of each SME which exists in an embedded business network to overcome the situation for SMEs which always have not or have not enough in providing accounting and associated asset information in the practice.By the feature of each Hologram for a given SME, one always has the related-party information in terms of either investment, or management dynamically, which is indeed also an explanation for the reason why the new approach proposed only comes true only until the era of big data’s occurring by using ideas from financial technology today.Furthermore, this paper explores the implementation of the “Holo Credit Loan”, a pure credit loan without any collateral and guarantee launched in 2016, as practical applications of the Hologram approach. We illustrate the framework of SMEs risk assessment under the Holograms new theoretical basis for solving the long-standing problem of credit risk assessment for SMEs (and individuals). Moreover, this paper’ conclusion will address the performance of the “Holo Credit Loan”.
introduced the notion of $L^0$--convex compactness for an $L^0$--convex subset of a Hausdorff top... more introduced the notion of $L^0$--convex compactness for an $L^0$--convex subset of a Hausdorff topological module over the topological algebra $L^0(\mathcal{F},K)$, where $K$ is the scalar field of real or complex numbers and $L^0(\mathcal{F},K)$ the algebra of equivalence classes of $K$--valued measurable functions defined on a $\sigma$--finite measure space $(\Omega,\mathcal{F},\mu)$, endowed with the topology of convergence locally in measure. A complete random normed module $($briefly, $RN$ module$)$, as a random generalization of a Banach space, is just such a kind of topological module, this paper further introduces the notion of random normal structure and gives various kinds of determination theorems for a closed $L^0$--convex subset to have random normal structure or $L^0$--convex compactness, in particular we prove a characterization theorem for a closed $L^0$--convex subset to have $L^0$--convex compactness, which can be regarded as a generalization of the famous James characterization theorem for a closed convex subset of a Banach space to be weakly compact. Based on these preparations, we generalize the classical Kirk's fixed point theorem from a Banach space to a complete $RN$ module as follows: Let $(E,\|\cdot\|)$ be a complete $RN$ module and $V \subset E$ a nonempty $L^0$--convexly compact closed $L^0$--convex subset with random normal structure, then every nonexpansive self--mapping $f$ from $V$ to $V$ has a fixed point in $V$. The generalized Kirk's fixed point theorem is also of fundamental importance in random functional analysis, for example, we can derive from it a very general random fixed point theorem, which unifies and improves several known random fixed point theorems for random nonexpansive mappings.
The goal of this paper is to develop some fundamental and important nonlinear analysis for single... more The goal of this paper is to develop some fundamental and important nonlinear analysis for single-valued mappings under the framework of p-vector spaces, in particular, for locally p-convex spaces for 0 < p ≤ 1. More precisely, based on the fixed point theorem of single-valued continuous condensing mapping in locally p-convex spaces as the starting point, we first establish best approximation results for (single-valued) continuous condensing mappings which are then used to develop new results for three classes of nonlinear mappings consisting of 1) condensing; 2) 1-set contractive; and 3) semiclosed 1-set contractive mappings in locally p-convex spaces. Next they are used to establish general principle for nonlinear alternative, Leray - Schauder alternative, fixed points for non-self mappings with different boundary conditions for nonlinear mappings from locally p-convex spaces, to nonexpansive mappings in uniformly convex Banach spaces, or locally convex spaces with Opial condit...
The goal of this paper is to establish a general fixed point theorem for upper semicontinuous set... more The goal of this paper is to establish a general fixed point theorem for upper semicontinuous set-values mappings in p-vector spaces (p∈(0, 1]), which include topological vector spaces as a special class. These new results provide an answer to Schauder conjecture in the affirmative under the setting of p-vector spaces for set-valued mappings, which would be fundamental for nonlinear functional analysis in mathematics. AMS Classification: 47H04, 47H10, 46A16, 46A55, 49J27, 49J35, 52A07, 54C60, 54H25, 55M20
International Journal of Intelligent Systems, Apr 6, 2021
The purpose of this paper is to establish a generalized dynamical framework for small and micro‐e... more The purpose of this paper is to establish a generalized dynamical framework for small and micro‐enterprise (SME) growth in the tech‐economic paradigm, and develop a novel quantitative method for the decision‐making of optimal equity and capital structure under the measurement of dynamical risk profiles. Based on the numerical simulations in different scenarios, we systematically study the dependence of SME growth performance on various factors, including capital structure, investment preference, and internal risk level, and find that dynamical optimal equity structure always corresponds to the better performance on value at response risks, and significantly reduces the bilateral cooperative risk at the inconspicuous cost of systematic response risk. Moreover, it is also observed that SME state behaves some important nonmonotonous features, such as stochastic resonance with internal risk level, generalized stochastic resonance with operating capital leverage. These results will provide the latent support for SMEs to create useful decision rules in capital optimization, risk management, and growth path regulation.
Communications in computer and information science, 2019
The goal of this paper is to introduce a new notion called “Consensus Game (CG)” with motivation ... more The goal of this paper is to introduce a new notion called “Consensus Game (CG)” with motivation from the mechanism design of blockchain economy under the consensus incentives from Bitcoin ecosystems in financial technology (Fintech), we then establish the general existence results for consensus equilibria of consensus games in terms of corresponding interpretation based on the viewpoint of Blockchain consensus in Fintech by applying the concept of hybrid solutions in game theory. As applications, our discussion in this paper for the illustration of some issues and problems on the stability of mining pool-games for miners by applying consensus games shows that the concept of consensus equilibria could be used as a fundamental tool for the study of consensus economics under the framework of Blockchain economy in Fintech.
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