Negative probabilities - Can we have negative payments in bonds? In Half of a Coin: Negative Probabilities, the author mentions bond duration.

Suppose we have payments at times $t = 1,2,...,n$ denoted respectively by $R_1, R_2, ..., R_n$ and the discount factor is $v = \frac{1}{1+i}$ where $i$ is effective interest rate. Then the bond value today is given by

$$B = \sum_{t=1}^{n} R_tv^t$$

The bond duration is

$$D = \frac{\sum_{t=1}^{n} tR_tv^t}{\sum_{t=1}^{n} R_tv^t}$$

It can be seen that $$D = E[T]$$

where

$T$ is a random variable with range $t = 1,2,...,n$ each having probability $\frac{R_t v^t}{B}$

The author says something like we can have negative probabilities if we have negative $R_t$'s. So this is a kind of bond where instead of making a payment we get a certain amount of money? Is there such a thing? Or is that only in theory?
I heard in a lecture at my university, that measure theory is applied in finance. This field also operates with negative probabilities a lot.

Anyways, I don't see the practical intuition behind using negative probabilities in a bond-pricing model. You can check this article by Burgin and Meissner: Negative Probabilities in Financial Modeling (Wilmott Magazine March 2012).

I think you should migrate your question to Quant SE.