hi,I have some trivial question about Piterbarg seminal paper on how funding and collateralisation impacts Black and Scholes PDE.The paper can be found here :paperalso, just below equation (4) he states the following :"Note that if our probability space is rich enough, we can take it tobe the same risk-neutral measure P as used in (1)."What does it mean exactly ? What are the technical assumptions behing the "rich enough" comment ?Many thanksApprentice

so we have the PDE just above (3). We know by Feyman Kac that the solution can be represented by (3), (4) for some Brownian motion W_S. But this Brownian motion needs to "live" in some probability space. It is convenient to have this BM on the same probability space as W_C from (1). There isn't really any theoretical asumptions here as we can clearly find a probability space that can host both W_S and W_C. the sentence should be understood as "when we mentioned the probability space for W_C we implicitly assumed that there is room there for one more Brownian motion"hope this clarifies matters.. if it does not, I suggest thta you not worry about it. It is really a pretty obscure point that betrays my upbringings in the rigorous world of pure math and that I could not resist throwing into an applied finance paper! sorry about itVladimir

hi Vladimir.thank you very much for the explanation.I got it now.I agree that it does not hinder in any way the understanding of your article, I was just curious about why it was mentionned when most papers do not mention these technical details. I thought I was maybe missing some specific subtle point.