Advanced Stochastic Processes
نویسنده
چکیده
We continue with the assumptions used in the previous lecture that price of a security can be modeled as an Ito process. Assume we have N price processes dXj = μj (t)dt + σj (t)dB(t), j = 1, 2, . . . , N . We assume that B is a vector of d independent Brownian motions and each σj is ddimensional vector process as well (for simplicity we skip the · notation from here onwards). We recall that this Brownian motion is adapted to some filtration Ft on a probability space (Ω,F ,P). Recall that a probability measure P∗ is equivalent to P if P(A) > 0 iff P∗(A) > 0 for all A ∈ F , and any such measure P∗ can be obtained via some random variable ψ = d d P P ∗ .
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تاریخ انتشار 2005