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Simplicio,I don't think so. For now the market price of risk = (u(s)-r)/sigma is not a constant, the market price of risk are also random variable. I think in a risk-netual market the market price of risk should be the same , or the market would be incomplete, and martingale wouldn't be no useful.

In fact, the market price of risk does not have to be constant... it can be a deterministic function of time... my question is whether or not we can extend this to introduce stochastic drifts into brownion motions... by reading the material in different texts, I would be very surprised if we can introduce stochastic drifts using the usual Girsanov theorem... I thougth that the Girsanov theorem only allows introduction of deterministic (or constant) drifts. But I need some confirmation on this and an intuitive explanation why this is so... I can see it mathematically... but not logically!!Sam

The drift can be random.

Nick Webber wrote a paper on this topic. Upshot is that a stochastic drift does not affect option pricing.MJ

Do you have Nick Webber 's paper? If someone has it , please paste it there or just mail to me:amoy_parsa@hotmail.com

The Martingale line of attack is MUCH weaker than I had thoughtand they lead to weak solutions.On the other hand, I'm currently working with Girsarnov Theorem. I know that I need to show L^2, as well as Nivarkov condition. Are there any other condition's that I should worry about?

Maybe the following link provides some additional info:http://www.cwi.nl/~neumann/download/jumpdif.pdfIt's another angle on arriving at option prices than using martingales,maybe it adds some insight in changing measures and such...There is a nice formula Eq. 29. This is a general solution for a European option withtime-dependent drift and vols, and constant jumpsizes in a complete jump-diffusion setting. It provides the price in its canonical form without making any reference to a particular measure.Of course you can pick your favorite measure and cast the equation in the form of an expectation. Take care,JiriJump-diffusion paper

I found the way you explain the drift very comprehensive and interesting. As a beginner it helped me in understanding the Martingale concept some more. I really wonder the next chapter. I would appreciate if you could go on with the same methodology and analogy you have developed. Thanks a lot.

Now why are working with martingales inportant?That is the next chapter in the story! If this is interesting at all, let me know and I'll continue. Otherwise, I'll just concentrate on conquering the world of math finance by myself.Hi,I found the way you explain the drift very comprehensive and interesting. As a beginner it helped me in understanding the Martingale concept some more. I really wonder the next chapter. I would appreciate if you could go on with the same methodology and analogy you have developed. Thanks a lot.