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to answer my own question, there's no popular model for the question, that $dS/S=\mu(t)dt+\sigma(t)dW$, and $\sigma(t)$ is correlated with $\mu(t)$. the general framework should be stochastic volatility model, but need do the extension on my own.


I got a solution to this problem by posting an excerpt of it at math.stackexchange: http://math.stackexchange.com/questions/716242/equation-involving-expectations-of-levy-processes

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