frolloos wrote:Until you run into a problem that can't be solved by PDE methods..

Or can *all* pricing questions be solved by PDE methods and hence true that no measure change necessary at all?

Suppose we live in a discrete-time world where stock prices only change in a trinomial way: up, down, or unchanged. Then, what can you say about option prices?

I believe it was these kinds of questions that got people thinking, post-Black-Scholes paper -- what is the more general theory that BS have partially discovered in a very specific model (GBM)?

Of course, pre-Black-Scholes, there was a lot of general theory about options and the best thinking used the notion of "util-probs" (Samuelson-Merton, 1969). Post-BS, this morphed into "measure change", a trivial change in nomenclature but accompanied by a deeper theory.

Can we have a general theory of option/securities valuation without mentioning util-probs/measure change? I doubt it because fundamentally:

- investors are risk-averse, and

- markets are not complete.