Mathematical Modeling in Finance with Stochastic Processes

6.3. PROPERTIES OF GEOMETRIC BROWNIAN MOTION 213

3. What is the probability that Geometric Brownian Motion with param-
   etersμ= 0 andσever rises to more than twice its original value? In
   economic terms, if you buy stock whose fluctuations are described by
   Geometric Brownian Motion, what are your chances to double your
   money?


4. Derive the probability of ruin (the probability of Geometric Brownian
   Motion hittingA <1 before hittingB >1).

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