# Why not discount the dividend in the european put lower bound condition?

According to the european put lower bound condition:

$$p \geq max(D + K \cdot e^{-r(t_2-t_0)} - S_0, 0)$$

where $$t_0$$ is now and $$t_2$$ is maturity. Say $$t_1$$ is the dividend release time where $$t_0.

Shouldn't it be:

$$p \geq max(D \cdot e^{-r(t_1-t_0)} + K \cdot e^{-r(t_2-t_0)} - S_0, 0)$$ ?

The common proof when it comes to portfolio B consists of investing $$D + K \cdot e^{-r(t_2-t_0)}$$ at the risk-free rate. (Portfolio A is going long on a put and the asset. The 2 portfolios' cashflows are compared and it is shown that since $$P_A \geq P_B$$ at $$t_2$$ that should stand for $$t_0$$ as well.)

$$D \cdot e^{-r(t_1-t_0)} + K \cdot e^{-r(t_2-t_0)}$$ in order to get equal cashflows $$(=D)$$ at time $$t_1$$? I.e. discounting the divident in the same fashion with the strike but at its respective time-frame?
• Be very careful how $D$ is defined in the book/article you are referencing. Sometimes $D$ is defined as the present value of the dividend, i.e. it has already been discounted from the ex-dividend date to the present. – noob2 May 18 at 16:44