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It sounds to me like you have a Markov model that is not "lumped", it's just that certain transitions don't provide you with any payout. I would model the true transition probabilities. Now, let's ask what the probability of getting a one is, assuming that we won't stay at zero, i.e. $P(X_1=1 | X_0=0, X_1 \not = 0)$. We recall that $$P(A|B)=P(A,B) / P(B)$$ ...


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The following paper gives you a step-by-step presentation of how to use the Kalman filter in an application in a pricing model framework for a spot and futures market. Everything is explained using Excel: A Simplified Approach to Understanding the Kalman Filter Technique by T. Arnold, M. Bertus and J. M. Godbey


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1) Analysis of Financial Time Series by Ruey Tsay 2) An Introduction to Bayesian Inference in Econometrics by Arnold Zellner Not finance specific, but this is the best multivariate stats book I know of: 3) Applied Multivariate Statistical Analysis by Johnson and Wichern


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Elements of Statistical Learning by Hastie, Tibshirani and Friedman is one of the most-cited books for your purpose. Although it does not have any direct applications to Finance, this is definitely a good book to have in your professional library and can be used as a reference for most topics. If you want to use a book with more financial applications, I ...


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I think a good book to start in your case is: Attilio Meucci: Risk and Asset Allocation I once had a seminar held by Attilio that was based on the book and it blew my mind. The book is very intuitive yet rigorous.


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I would highly recommend this books: Mathematics and Statistics for Financial Risk Management: Book 1 The other one, is Chapter three from, Practical Methods of Financial Engineering and Risk Management: Tools for Modern Financial Professionals: Book 2 Hope it helps.



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