The prices for two stocks evolve as the processes S t1 10exp 1 w t1 and S t2 11exp 2 w t2 , where w t1 and w t2 are independent Brownian motions, 1 0 1, and 2 0 2 What are the initial prices for the stocks Find the probability that during a year the price S t1 will meet the price S t2

Question: The prices for two stocks evolve as the processes S t1 =10exp{ 1 w t1 } and S t2 =11exp{ 2 w t2 }, where

The prices for two stocks evolve as the processes S_t1 =10exp{σ₁w_t1} and S_t2 =11exp{σ₂w_t2}, where w_t1 and w_t2 are independent Brownian motions, σ₁ = 0.1, and σ₂ = 0.2. What are the initial prices for the stocks? Find the probability that during a year the price S_t1 will meet the price S_t2.

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