Question: Ito's rule: Example 3 Compute ESt? Solution 1: If X ~ N(m, v) then Eex = emto/2 so ESt = Soent Solution 2: Take expectations

Ito's rule: Example 3 Compute ESt? Solution 1: If X ~ N(m, v) then Eex = emto/2 so ESt = Soent Solution 2: Take expectations of both sides of St = Sot MSudu+/ " Sudwu = ESt = So + MESudu + 0 o m(t) = So + um(u) du where m(t) := ESt. Differentiate both sides wrt t, to get m' ( t ) = um (t ) m (0 ) = So Solution to this ODE: m(t) = Spent

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