Question: These problems are relevant to stochastic finance, please help me to solve it. Thanks a lot! Problem 3 Consider the geometric Brownian motion Xt =

These problems are relevant to stochastic finance, please help me to solve it. Thanks a lot! Problem 3 Consider the geometric Brownian motion

These problems are relevant to stochastic finance, please help me to solve it. Thanks a lot!

Bt. Compute E [Xt], Var [X.], E [Xt|Fs], Var [X.|Fs] for s

Problem 3 Consider the geometric Brownian motion Xt = cutto Be Let It be the natural filtration associated with Bt. Compute E [Xt], Var [X.], E [Xt|Fs], Var [X.|Fs] for s s where Be is the standard Brownian motion. Problem 7 1. Calculate E[B Bs|Fs] for t > s where Be is the standard Brownian motion.. 2. Calculate E[B?|F,] for t 2 s where Be is the standard Brownian motion.. 3. Suppose that B? - ct is a martingale with respect to the natural filtration of the Brownian motion Bt. Find c

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