$$ \require{enclose} \enclose{box}{ \begin{array}{c} \ 交易前: \ x=1000 \ y=5000\ \ K=5000000\ \ \end{array} } \underrightarrow{\quad\bf用100个A购买B\quad} \enclose{box}{ \begin{array}{ccccccc} \ 交易后: \ x^1=1100 \ K=5000000\ \ y^1=K/x^1\approx4545.45\ \
\end{array}
} \qquad\bf获得B数y_1为454.55(y-y^1) $$
交易后K值不变（0.3%手续费）$$ \require{enclose} \enclose{box}{ \begin{array}{c} \ 交易前: \ x=1000 \ y=5000\ \ \ K=5000000\ \ \ \end{array} } \underrightarrow{\quad\bf用10个A购买B\quad} \enclose{box}{ \begin{array}{ccccccc} \ 交易后: \ x^f=(1000+100*0.997) \ x^1=(1000+100) \ y^1=K/x^f\approx4546.69 \ \
K=50000\\
K^1=x^1*y^1\approx5001359\\
\\
\end{array}
} \qquad\bf获得B数y_1为453.31(y-y^1) $$
-
初始提供
$$ \require{enclose} \enclose{box}{ \begin{array}{c} \ 提供前: \ x=0 \ y=0\ \ L=0\ L_m=1000\ \ \end{array} } \underrightarrow{\quad\bf提供100个A和500个B的初始流动性\quad} \enclose{box}{ \begin{array}{ccccccc} \ 提供后: \ x=1000 \ y=5000\ \ \ L=\sqrt[2]{x*y}-Lm\ \
\end{array}} \qquad\bf获得初始流动性L=2236.07 $$
中途提供
$$ \require{enclose} \enclose{box}{ \begin{array}{c} \ 提供前: \ x=1000 \ y=5000\ \ L=2236.07\ L_m=1000\ \ \end{array} } \underrightarrow{\quad\bf提供100个A和500个B的流动性\quad} \enclose{box}{ \begin{array}{ccccccc} \ 提供后: \ x_1=100 \ y_1=500\ \ L_{x1}=x_1L/x\approx223.607\ L_{y1}=y_1L/y\approx223.607\ L^1=L+min(L_{x1},L_{y1})=2459.677\
\\ \\ \end{array}} \qquad\bf获得L_1=L^1-L=223.607 $$
$$ \require{enclose} \enclose{box}{ \begin{array}{c} \ 赎回前: \ x=1100 \ y=5500\ \ L=2459.677\ L_m=1000\ \ \end{array} } \underrightarrow{\quad\bf赎回223.607的流动性\quad} \enclose{box}{ \begin{array}{ccccccc} \ 赎回后: \ L_1=123.607 \ \ x_1=L_1x/L\approx100 \ y_1=L_1y/L\approx500\ x^{1}=x-x_1=1000\ y^{1}=y-y_1=5000\ L^1=L-L_1=2236.07\
\\
\\
\end{array}
} \qquad\bf获得A和B分别为100和500 $$
全部赎回$$ \require{enclose} \enclose{box}{ \begin{array}{c} \ 赎回前: \ x=1000 \ y=5000\ \ L=2236.07\ L_m=1000\ \ \end{array} } \underrightarrow{\quad\bf赎回所有流动性L-L_m\quad} \enclose{box}{ \begin{array}{ccccccc} \ 赎回后: \ L_1=1236.07 \ \ x_1=L_1x/L\approx552.79 \ y_1=L_1y/L\approx2763.93\ x^{1}=x-x_1=447.21\ y^{1}=y-y_1=2236.06\ L^1=L-L_1=1000\
\\
\\
\end{array}
} \qquad\bf亏损了初始流动性销毁了L_m的流动性 $$