content_image/316447.jpg content_image/316446.jpg content_image/316445.jpg content_image/316444.jpg content_image/316443.jpg
y , we can use the monotone convergence theorem to obtain 

<img src='content_image/316447.jpg'>

Thus, due to the definition of an admissible pricing rule, we have 

<img src='content_image/316446.jpg'>

The same argument can be applied to the left derivative of V with respect to y to obtain 

<img src='content_image/316445.jpg'>

As a consequence, we can express E [ X θ 1 ] in terms of V as (notice that ∫ t 0 B 2 $_{t}$dF ( Z$_{t}$, t ) is a martingale) 

<img src='content_image/316444.jpg'>

On the other hand, by applying the Itˆ o formula for semimartingales to V directly ([14], Theorem II.6.33, p. 81) we get 

<img src='content_image/316443.jpg'>

Notice that, due to the definition of the fundamental value F and of admissible pricing rule 

