Let S(t) be a positive stochastic process that satisfies the generalized geo- metric Brownian motion differential equation
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Let S(t) be a positive stochastic process that satisfies the generalized geo- metric Brownian motion differential equation
dS(t)-a(t)S(t)dt + (t)S(t)dW'(t)
where a(t) and (t) are processes adapted to the filtration F(t), t associated with Brownian motion W(t), t 0, 20
a. Use It formula to compute d (log(S(t)) Simplify so that you have a formula for d (log(S(t)) that does not involve S(t).
b. Integration the formula in a. and then exponentiate to obtain the solution.
Related Book For
Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook
ISBN: 9783110741254
3rd Edition
Authors: René L. Schilling, Björn Böttcher
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