Expectation of a dt term

Asked Jun 13 '22 at 17:19

Active Jun 13 '22 at 17:19

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I am working with Hamilton-Jacobi-Bellman Equations and the following result appeared.

Suppose $V_t= \frac{\partial V}{\partial t}$

and that $ E_{t}[Y]=E\left[Y \mid F_{t}\right] $ , where $F_t$ represents the information at time t

I do not understand why the following holds:

$E[V_t dt]=V_t$

You could write the expectation as an integral but this didn't clearify anything for me

asked Jun 13 '22 at 17:19

WHN

2

Why do you believe that $E[V_t dt] = V_t$? – Michael Jun 13 '22 at 17:27
It is written in the book – WHN Jun 13 '22 at 18:06
I am guessing the book intended to write $E[V_t|F_t]=V_t$, assuming $V_t$ is $F_t$-measurable. – Michael Jun 13 '22 at 21:12

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