Research on Dynamic Prediction Model of Consumer Credit Risk under Fintech Innovation

Big data technology is an advanced technology for processing and analyzing massive data sets, especially referring to those data that exceed the processing capacity of traditional databases. It relies heavily on sophisticated data processing software that can quickly analyze, process, and extract valuable information.

In the banking industry, the application of big data technology is becoming increasingly broad and deep. First, it plays an important role in risk management, enabling more effective identification and management of credit and market risks. Second, in terms of customer service, big data technology helps banks analyze customer needs and provide more personalized services. In addition, big data technology plays a key role in banks’ marketing strategies. By analyzing customer data, banks can design more accurate marketing campaigns. Also, big data technology is very effective in preventing financial fraud. Finally, big data technology also helps banks improve their internal operational efficiency.

Blockchain technology is a distributed ledger technology that makes data transmission secure and reliable in a decentralized network. In this network, data is stored in the form of blocks connected by encrypted chains, with each new block containing encrypted information from the previous block, thus ensuring data immutability and transparency. This structure makes blockchain an ideal system for recording and sharing data. In the banking industry, blockchain technology is mainly used to improve transaction efficiency and security.

Artificial Intelligence (AI) technology mimics human thought processes, including the ability to learn, reason, self-correct, and automate decision-making utilizes algorithms and large amounts of data to enable machines to solve complex problems and perform specific tasks. In the banking industry, AI is used to improve service efficiency and customer experience.

Cloud computing is a technology that provides computing resources and data storage services over the Internet. It allows users to access and use software, storage, and other computing functions located on remote servers over the Internet without having to manage physical servers or run application software locally.

In the banking industry, the use of cloud computing is growing, revolutionizing this traditional industry. First, cloud computing provides powerful data processing capabilities that help banks efficiently handle large amounts of transaction data and enable fast, accurate data analysis. Second, cloud computing helps banks cope with business fluctuations by providing flexible resource allocation. In addition, cloud computing supports innovation in the banking industry. Finally, cloud computing also plays a key role in improving the security and compliance of banking operations.

Consumer loans specifically refer to loan services provided by banks or other financial institutions to individual consumers with a defined consumption purpose. Such loans are mainly based on the borrower’s credit history and future repayment ability and are used to satisfy their needs for purchasing consumer goods or paying for other personal consumption.

Thanks to personal consumer credit, public deposit funds can be further circulated, which can effectively alleviate the financial pressure on families or individuals. Under the joint promotion of “consumption upgrading, policy support, and financial technology development”, China’s consumer credit system is becoming increasingly mature. According to the purpose of the loan, personal consumer credit can be categorized into housing and non-housing categories.

Consumer credit risk refers to the possibility that the borrower of personal consumer credit is unable to fulfill the repayment obligation according to the contract due to various uncertainties, thus exposing the commercial bank to the loss of funds [34]. This kind of risk runs through the three links of pre-credit, credit, and post-credit, including but not limited to incomplete pre-credit investigation, non-compliance of credit review, as well as untimely and unstandardized post-credit management. When the borrower defaults, commercial banks will face the risk of non-performing loans, which will affect their asset quality and operational stability.

The characteristics of consumer credit risk mainly include: First, the diversity of risk sources, which may come from the borrower’s own credit risk but also from the market environment, policy adjustment, and other external factors. Second, the risk is hidden. Part of the risk may be difficult to detect at the beginning of the loan but gradually exposed over time. Thirdly, risks are contagious, and once a risk arises in a certain link, it may spread to the entire credit chain and affect the overall operation of the bank.

Assuming that T denotes the survival time of a single individual in a population and is a continuous type non-negative random value covering the range [0,∞], the probability F(t) of the cumulative distribution function of T is given by the following equation: 1 F(t)=P(T≤t)=∫0tf(x)dx,∀t≥0

In contrast, the probability of an individual surviving longer than time t is the survival function, whose probability model S(t) is shown below: 2 S(t)=P(T>t)=1−F(t)=∫t∞f(x)dx,∀t≥0

S(t) is a monotonically decreasing continuous function. where S(0) = 1, denotes the probability that an individual survives beyond the starting point 0, and S(∞)=limt→∞S(t)=0, denotes the probability that an individual survives for an infinite amount of time.

If first-order differentiation is done on F(t), then the probability function of death for survival time T can be obtained, denoting the magnitude of the probability of death occurring at any infinitesimal time from t to t + Δt when the individual uses time as a variable, denoted by f(t), and whose probability equation is expressed in the following equation: 3 f(t)=dF(t)dt=−dS(t)dt=limΔt→0+P(t<T<t+Δt)Δt,∀t≥0

Another way of describing the magnitude of the probability of death in the survival analysis approach is to express the degree of risk or instantaneous mortality that an individual may die, called the risk function when it is known that the individual is still alive at the moment of t, but the probability of death occurring in a subsequent very small unit of time Δt is expressed as a probability equation in h(t): 4 h(t)=limΔt→0+P(t<T<t+Δt|T>t)Δt=f(t)S(t),∀t≥0

From equations (1) and (2) we know f(t)=–F(t), so the above equation can be rewritten as: 5 h(t)=f(t)S(t)=−dS(t)dtdt=−dlogS(t)dt,∀t≥0

The survival function is then obtained by taking the integral of the above equation and converting it to exponential form: 6 ∫0th(x)dx=−logS(t)

Also i.e., for: 7 S(t)=exp(−∫0th(x)dx)

Then, based on the relationship between the functions, the probability density function of an individual at time point t can then be obtained: 8 f(t)=h(t)S(t)=h(t)exp(−∫0th(x)dx)

Similarly, assuming that T represents the survival time of a single sample in the aggregate and is a discrete non-negative random value, denoted by t₁,t₂,t₃,... , etc., where 0 < t₁ < t₂ < t₃ <..., the probability function is: 9 P(ti)=P(T=ti),i=1,2,3,…

At this point, the survival function is represented by the following equation: 10 S(t)=P(T≥t)=∑i:ti≥tP(ti)

where S(t) is a monotonically decreasing function, S(0)=1, S(∞)=0.

The risk function h(t) can be expressed as: 11 h(t)=P(T=ti|T≥ti)=P(ti)S(ti),i=1,2,3,…

From the above equation, we know that P(t_i) = S(t_i)–S(t_i+1).

So equation (11) can be rewritten as: 12 h(ti)=1−S(ti+1)S(ti),i=1,2,3,…

Also ie: 13 S(t)=∏i:ti<t[ 1−h(ti) ],i=1,2,3,…

Let the density function of survival time T be f(t|X) and the survival function be S(t|X) when the covariate is X. The hazard rate function is: 17 λ(t|X)=f(t|X)S(t|X)

If X₁ ≠ X₂, then ratio λ(t|X1)λ(t|X2) is independent of t. The relationship between survival time T and covariate X is said to fit the proportional risk rate model, so for this model, the hazard rate for survival time T has the following form: 18 S(t|X)=exp{ −∫0tλ(μ|X)dμ }

Here λ₀(t) is called the benchmark risk rate due to the survival function of T: 19 S(t|X)=exp{ −∫0tλ(μ|X)dμ }

From equation (18): 20 S(t|X)=[ S0(t) ]g(X)

where S0(t)=exp{ −∫0tλ0(μ)dμ }.

It follows from Eq. (20) that for all X₁, X₂, or S(t|X₁)≥S(t|X₂), or S(t|X₁)≤S(t|X₂), which indicates that the survival times are randomly comparable for different values of the covariates.

In practical problems, g(X) in Eq. (20) is often chosen to be in parametric form, i.e., g(X) = g₀(X,β). Where here g₀ is the known function, X = (x₁,...x_p)^T is the covariate, and β = (β₁,...,β_p)^T is the unknown parameter. In this case, Eq. (20) simplifies to: 21 S(t|X)=[ S0(t) ]g0(X,β)

Equation (21) is called the generalized Cox model. When g₀ (X,β) = exp{X^T β}, Eq. (21) is called the Cox proportional risk model, which was proposed by the British statistician Cox in 1972. There are two important parameters in Eq. (21), one is parameter β and the other is the baseline survival function S₀(t), thus the model is a semiparametric model, and both of the so far parameters need to be estimated from observed data.

The so-called proportional risk assumption test, or PH assumption, means that the effect of covariates in the model does not change with time. That is to say, in the model, the risk function of different individuals is proportional to each other [37]. The test of the PH assumption is necessary before building the Cox proportional risk model. Only through the PH assumption the model built is valid; otherwise, it is invalid. If the PH assumption is not satisfied, on the one hand, the changed significance due to the existence of variables that do not satisfy the PH assumption receives a corresponding effect. Secondly, if the risk ratio increases with time, then the relative hazard ratio is overestimated, and if the opposite occurs, the relative hazard ratio is underestimated.

In academic research, common methods for testing PH assumptions include the graphical method and the test method.

For the parameter part of the Cox proportional risk model, this paper adopts the partial likelihood estimation method. Assuming a sample size of n, i.e., the survival time of n listed firms is observed, three variables are included in the sample data, namely, X_i, δ_i, and T_i, where X_i is the covariate of the ith firm and T_i is its survival time. When the true survival time of a listed firm is greater than t_i, it means that the firm did not experience financial distress during the study period, which is denoted as δ_i = 0;. On the contrary, when the true survival time of a listed firm is t_i, then it means that the listed firm did not experience financial distress during the study period, which is denoted as δ_i = 1. Therefore, the observations of interest are represented by a set, i.e.: 22 (ti,δi,Xi),i=1,2,⋯,n

Let t₁ < t₂ < … < t_n denote the order of survival times. Define the risk set at time t_i to be R(t_i):{t_j > t_i}, which represents the set of all individuals still in the study process until t_i. The principle of partial likelihood estimation to estimate the parameters of the model covariates will be briefly described below.

If an individual in R(t_i) dies at time t_i, i.e., financial distress occurs, then the conditional probability of death at time t_i for an individual with covariate X_i is, given this condition: 23 P[ individualdiedatmomentti|anindividualdiedatmomentti ]=h[ ti|Xi ]∑j∈R(t)h[ ti|Xj ]=h0(ti)exp[ β′Xi ]∑j∈R(ti)h0(ti)exp[ β′Xj ]=exp[ β′Xi ]∑j∈R(ti)exp[ β′Xj ]

Multiplying the conditional probabilities of death at all time points gives the partial likelihood function, shown in equation (24): 24 L(β)=∏i=1nexp[ β′Xi ]∑j∈R(ti)exp[ β′Xj ]

Taking logarithms of Eq. (24) and solving for derivatives makes: 25 ∂lnL(β)∂β=0

The great likelihood estimate of parameter β from the partial likelihood estimation method can be obtained by solving equation (25).

Once the estimate of parameter β is obtained by the partial likelihood estimation method, the next step is the estimation of the baseline survival function. In the Cox proportional risk model, the benchmark survival function S₀(t) is a nonparametric form, and there are two main methods for its estimation: