# 基于多状态Markov模型的企业财务困境预测研究Research on Financial Distress Prediction Based on Multi-State Markov Model

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Based on the multi-state Markov model, the financial distress prediction problem of listed com-panies is studied. First, a multi-state Markov model is constructed. Then, based on the multi-state Markov model, we construct an exponential model with covariables of financial distress factors. Finally, the financial dilemma of listed companies is forecasted from the two aspects of transition probability and residence time. The results show that the multi-state Markov model can be applied to the prediction of financial distress and can reveal the evolution of financial distress.

1. 引言

2. 多状态Markov模型构建

3. 指数模型

Figure 1. Multi-state Markov model transfer flow chart

(观察对象编号，状态，观察时刻，协变量1，协变量2……)

$Q=\left(\begin{array}{cccc}0& 0.5& 0.01& 0\\ 0.3& 0& 0.166& 0\\ 0.01& 0.01& 0& 0.04\\ 0& 0& 0& 0\end{array}\right)$ (1)

3.1. 多状态多因素Markov模型拟合结果

3.2. Markov指数模型

${q}_{ij}\left(Z\right)={q}_{ij0}\mathrm{exp}\left[{\sum }_{k=1}^{n}{\beta }_{ijk}{Z}_{k}\right]$ (2)

Table 1. Multi-factor and multi-state Markov model fitting results

$\begin{array}{c}{q}_{12}\left(Z\right)={q}_{120}\mathrm{exp}\left[{\sum }_{k=1}^{n}{\beta }_{12k}{Z}_{k}\right]\\ =0.413\mathrm{exp}\left[0.502×总资产净利率-0.064×流动比率+1.383×营运资金比率\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}-2.202×营业收入现金比率-0.101×存货周转率\right]\end{array}$ .

$\begin{array}{c}{q}_{13}\left(Z\right)={q}_{130}\mathrm{exp}\left[{\sum }_{k=1}^{n}{\beta }_{13k}{Z}_{k}\right]\\ =0.005\mathrm{exp}\left[-0.365×总资产净利率-0.843×流动比率-0.600×营运资金比率\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}-0.160×营业收入现金比率-0.332×存货周转率\right]\end{array}$ .

$\begin{array}{c}{q}_{21}\left(Z\right)={q}_{210}\mathrm{exp}\left[{\sum }_{k=1}^{n}{\beta }_{21k}{Z}_{k}\right]\\ =0.081\mathrm{exp}\left[2.096×总资产净利率-0.649×流动比率+1.453×营运资金比率\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+0.7441×营业收入现金比率+0.039×存货周转率\right]\end{array}$ .

$\begin{array}{c}{q}_{23}\left(Z\right)={q}_{230}\mathrm{exp}\left[{\sum }_{k=1}^{n}{\beta }_{23k}{Z}_{k}\right]\\ =0.017\mathrm{exp}\left[-2.007×总资产净利率+0.287×流动比率-0.989×营运资金比率\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}-0.144×营业收入现金比率-0.095×存货周转率\right]\end{array}$ .

$\begin{array}{c}{q}_{31}\left(Z\right)={q}_{310}\mathrm{exp}\left[{\sum }_{k=1}^{n}{\beta }_{31k}{Z}_{k}\right]\\ =0.001\mathrm{exp}\left[0.064×总资产净利率+0.252×流动比率+0.527×营运资金比率\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}-0.023×营业收入现金比率-0.005×存货周转率\right]\end{array}$ .

$\begin{array}{c}{q}_{32}\left(Z\right)={q}_{320}\mathrm{exp}\left[{\sum }_{k=1}^{n}{\beta }_{32k}{Z}_{k}\right]\\ =0.0007\mathrm{exp}\left[0.138×总资产净利率+0.372×流动比率+0.949×营运资金比率\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+0.186×营业收入现金比率+0.0004×存货周转率\right]\end{array}$ .

$\begin{array}{c}{q}_{34}\left(Z\right)={q}_{340}\mathrm{exp}\left[{\sum }_{k=1}^{n}{\beta }_{34k}{Z}_{k}\right]\\ =-0.029\mathrm{exp}\left[0.397×总资产净利率-0.271×流动比率+1.135×营运资金比率\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}-0.111×营业收入现金比率-0.0004×存货周转率\right]\end{array}$ .

4. 运用多状态Markov模型进行预测

4.1. 转移概率

Table 2. Matrix of transition probability (t = 1 year)

Table 3. Matrix of transition probability (t = 2 year)

Table 4. Matrix of transition probability (t = 5 year)

Table 5. Matrix of transition probability (t = 10 year)

4.2. 总停留时间

${L}_{S}={\int }_{{t}_{1}}^{{t}_{2}}P{\left(t\right)}_{r,s}\text{d}t$ 。其中，LS表示在时刻t1和t2之间处于状态s的总停留时间，r为财务状态变化发展过

5. 研究结论

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