Please recommend a textbook to prepare me for math research in econ

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Next semester I'll be doing some independent research in the mathematics of trading. Specifically I'm looking for a text that will teach me to grapple with Markov Chains, Brownian motion models, mean reversion models, and models with regime switching.
 

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Brownian motion like the bacterial movement observation? Might not be the answer you want with what follows except I'll tell you that if you're trying to do trading math you might chance a solution as to the trader's probability of trade actions except that's a guessing game. A reasoning for derivatives hedging is the sheer amount of capital invested into investment profiles before further trade agreements involving those derivatives ever takes place. They've got money. They use money to make estimated profit from the revenues of portfolios that are proven with statistics to be profitable. That's different than being guaranteed to be profitable.
 
Neuvotonian said:
Brownian motion like the bacterial movement observation? Might not be the answer you want with what follows except I'll tell you that if you're trying to do trading math you might chance a solution as to the trader's probability of trade actions except that's a guessing game. A reasoning for derivatives hedging is the sheer amount of capital invested into investment profiles before further trade agreements involving those derivatives ever takes place. They've got money. They use money to make estimated profit from the revenues of portfolios that are proven with statistics to be profitable. That's different than being guaranteed to be profitable.

I'm not quite sure what kinds of Brownian motion models I'll be using, but I think its safe to say they will have little to do with bacteria. However, the rest of your response actually seems quite relevant. My research will be directed by a faculty member and I think derivatives were mentioned as being a topic of special interest, so would you happen to know where I can find some course notes or other resources regarding your post?